Abel

Di NardoPetrulloSenato2010, Cumulants and convolutions via Abel polynomials, European J. Combin. Vol. 31, Issue 7, Oct 2010, 1792-1804, gen>

KayllPerkins2009, Combinatorial proof of an Abel-type identity, J. Combin. Math. Combin. Comput. 2009, vol.70: 33-40, jou>

KimKimLeeRim2013, Some identities of Bernoulli, Euler and Abel polynomials arising from umbral calculus, Adv. Difference Equ. 2013, 2013: 15, gen>

RotaShenTaylor1997, All polynomials of binomial type are represented by Abel polynomials, Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 25.3-4 (1997):  731-738, nat>

Akiyama-Tanigawa

Inaba2005, Hyper-sums of powers of integers and the Akiyama-Tanigawa matrix, J. Integer Seq. Vol. 8 (2005), Article 05.2.7, jis>

Kaneko2000, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Seq. Vol. 3 (2000), Article 00.2.9, jis>

MerliniSprugnoliVerri2005, The Akiyama-Tanigawa transformation, Integers 5 (2005), gen>

Zeng J.2006, The Akiyama-Tanigawa algorithm for Carlitz's q-Bernoulli numbers, Integers 6 (2006), gen>

Al-Salam-Carlitz

AskeySuslov1993, The q-harmonic oscillator and the Al-Salam and Carlitz polynomials, arXiv (9 jul 1993), aXv>

ChenSaadSun2009, An operator approach to the Al-Salam-Carlitz polynomials, arXiv (9 Oct 2009), arXiv>

Al-Salam-Chihara

IshikawaZeng2009, The partition function of Andrews and Stanley and Al-Salam-Chihara polynomials, Discrete Math. Vol. 309, Issue 1, Jan 2009, 151-175,  gen>

KasraouiStantonZeng2011, The combinatorics of Al-Salam-Chihara q-Laguerre polynomials, Advances in Applied Math. Vol. 47, Issue 2, Aug 2011, 216-239, gen>

Apery

Chang1984, A note on Apéry numbers, Fibonacci Quart. 1984 (22,2): 178-180, fibqy>

Glasser2012, A generalized Apéry series, J. Integer Seq. Vol. 15 (2012), Article 12.4.3, fibqy>

GuoZeng2012, New congruences for sums involving Apéry numbers or central Delannoy numbers, arXiv (25 May 2012), aXv>

JinDickinson2000, Apéry sequences and Legendre transforms, J. Austral. Math. Soc. (Series A) 68 (2000), 349-356, nat>

LucaShparlinski2008, Arithmetic properties of Apéry numbers, J. London Math. Soc. (2008) 78 (3):  545-562, nat>

Pan2014, On divisibility of sums of Apéry polynomials, J. Number Theory, Vol. 143, Oct 2014, 214-223, jou>

Pilehrood Kh.Pilehrood T.Tauraso2012, Congruences concerning Jacobi polynomials and Apéry polynomials and Apéry-like formulae, Int. J. Number Theory, 8 (2012), no. 7, 1789-1811, gen>

Schmidt1995, Legendre transforms and Apéry's sequences, J. Austral. Math. Soc. (Series A) 58 (1995), 358-375, nat>

Sun Z-W.2010a, On Apéry numbers and generalized cental trinomial coefficients, arXiv (19 Aug 2010), aXv>

Sun Z-W.2012a, On sums of Apéry polynomials and related congruences, J. Number Theory, Vol. 132, Issue 11, Nov. 2012, 2673-2699, jou>

Young1992, Apéry numbers, Jacobi sums, and special values of generalized p-adic hypergeometric functions, J. Number Theory 41, 231-255 (1992), jou>

Apostol

DereSimsek2011a, Unification of the three families of generalized Apostol type polynomials on the Umbral algebra, arXiv (7 Oct 2011), aXv>

LuLuo2013a, Some properties of the generalized Apostol-type polynomials, Bound. Value Prob. 2013, 2013:64-Proc. Int. Congress in Honour of Hari M. Srivastava, gen>

LuSrivastava2011, Some series identities involving the generalized Apostol type and related polynomials, Comput. Math. Appl Vol. 62, Issue 9, Nov 2011, 3591-3602, gen>

LuXiangLuo2013, Some results for Apostol-type polynomials associated with umbral algebra, Adv. Difference Equ. 2013, 2013:  201, gen>

MahmudovKeleshteri2014, q-extensions for the Apostol type polynomials, J. Appl. Math. Vol. 2014 (2014), Article ID 868167, 8 p, jou>

OzdenSimsek2014, Modification and unification of the Apostol-type numbers and polynomials and their applications, Appl. Math. Comput. Vol. 235, May 2014, 338-351, gen>

Wang Wei.Wang Wen2010, Some results on power sums and Apostol type polynomials, Integral Transforms Spec. Funct. Vol. 21, Issue 4, 2010, gen>

Apostol-Bernoulli

BagdasaryanAraci2013, Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis, arXiv (21 Nov 2013), aXv>

Kurt2013, Some relationships between the generalized Apostol-Bernoulli and Apostol-Euler polynomials, Turkish J. of Analysis and Number Theory 2013, Vol. 1, No. 1, 54-58, nat>

Luo2014, q-extensions of some results involving the Luo-Srivastava generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, Filomat 28:2 (2014), 329-351, gen>

LuoSrivastava2005, Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials, J. Math. Anal. Appl. Vol. 308, Issue 1, Aug 2005, 290-302, jou>

LuoSrivastava2006, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl. Vol. 51, Issues 3–4, Feb 2006, 631-642,

LuoSrivastava2011, Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind, Appl. Math. Comput. Vol. 217, Issue 12, Feb 2011, 5702–5728, gen>

Ozarslan2013, Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials, Adv. Difference Equations 2013, 2013: 116, gen>

SrivastavaOzarslanKaanoglu2013, Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, Russ. J. Math. Phys. Mar 2013, Vol. 20, Issue 1, 110-120, nat>

Wang J.2013, New recurrence formulae for the Apostol-Bernoulli and Apostol-Euler polynomials, Adv. Difference Equ. 2013, 2013: 247, gen>

Wang W.JiaWang T2008, Some results on the Apostol–Bernoulli and Apostol–Euler polynomials, Comput. Math. Appl. Vol. 55, Issue 6, Mar 2008, 1322-1332, gen>

Apostol-Euler

ChenCaiLuo2013, An extension of generalized Apostol-Euler polynomials, Adv. Difference Equ. 2013, 2013: 61, gen>

KimKimJang2008, On the q-extension of Apostol-Euler numbers and polynomials, Abstr. Appl. Anal. Vol. 2008 (2008), Article ID 296159, 10 p, gen>

Kurt2013, Some relationships between the generalized Apostol-Bernoulli and Apostol-Euler polynomials, Turkish J. of Analysis and Number Theory 2013, Vol. 1, No. 1, 54-58, nat>

Luo2006, Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions, Taiwanese J. of Math. Vol. 10, No. 4, 917-925, 2006,  nat>

Luo2014, q-extensions of some results involving the Luo-Srivastava generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, Filomat 28:2 (2014), 329-351, gen>

LuoSrivastava2005, Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials, J. Math. Anal. Appl. Vol. 308, Issue 1, Aug 2005, 290-302, jou>

LuoSrivastava2006, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl. Vol. 51, Issues 3–4, Feb 2006, 631-642, jou>

SrivastavaOzarslanKaanoglu2013, Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, Russ. J. Math. Phys. Mar 2013, Vol. 20, Issue 1, 110-120, nat>

TrembleyGabouryFugčre2012, Some new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials, Int. J. Math. Math. Sci. Vol. 2012 (2012), Article ID 182785, 14 p, gen>

Wang J.2013, New recurrence formulae for the Apostol-Bernoulli and Apostol-Euler polynomials, Adv. Difference Equ. 2013, 2013: 247,  gen>

Wang W.JiaWang T.2008, Some results on the Apostol–Bernoulli and Apostol–Euler polynomials, Comput. Math. Appl. Vol. 55, Issue 6, Mar 2008, 1322-1332, gen>

Apostol-Genocchi

BagdasaryanAraci2013, Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis, arXiv (21 Nov 2013), aXv>

JolanySharifiAliKelayie2013, Some results for the Apostol-Genocchi polynomials of higher order, Bull. Malays. Math. Sci. Soc. (2) 36(2) (2013), 465-479, nat>

Luo2009b, q-extensions for the Apostol-Genocchi polynomials, General Math. Vol. 17, No. 2 (2009), 113-125, gen>

Luo2014, q-extensions of some results involving the Luo-Srivastava generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, Filomat 28:2 (2014), 329-351, gen>

LuoSrivastava2005, Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials, J. Math. Anal. Appl. Vol. 308, Issue 1, Aug 2005, 290-302, jou>

LuoSrivastava2006, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl. Vol. 51, Issues 3–4, Feb 2006, 631-642, jou>

LuoSrivastava2011, Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind, Appl. Math. Comput. Vol. 217, Issue 12, Feb 2011, 5702-5728, gen>

Ozarslan2013, Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials, Adv. Difference Equations 2013, 2013: 116, gen>

SrivastavaOzarslanKaanoglu2013, Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, Russ. J. Math. Phys. Mar 2013, Vol. 20, Issue 1, 110-120,  nat>

SrivastavaOzarslanYilmaz2014, Some families of differ. equat. assoc. with the Hermite-based Appell polyn. and other classes of Hermite-based polyn., Filomat 28: 4 (2014), 695-708, gen>

TrembleyGabouryFugčre2012, Some new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials, Int. J. Math. Math. Sci. Vol. 2012 (2012), Article ID 182785, 14 p,  gen>

Wang J.2013, New recurrence formulae for the Apostol-Bernoulli and Apostol-Euler polynomials, Adv. Difference Equ. 2013, 2013: 247, gen>

Wang W.JiaWang T.2008, Some results on the Apostol–Bernoulli and Apostol–Euler polynomials, Comput. Math. Appl. Vol. 55, Issue 6, Mar 2008, 1322-1332, gen>

Appell

AcetoMalonekTomaz2014, A unified matrix approach to the representation of Appell polynomials, arXiv (3 Jun 2014), aXv> aXv>

Anshelevich2009a, Appell polynomials and their relatives II. Boolean theory, Indiana Univ. Math. J. 58 (2009), 929-968, nat>

Anshelevich2009b, Appell polynomials and their relatives III. Conditionaly free theory, Illinois J. Math. Vol. 53, No. 1, Spring 2009, 39-66, nat>

BrettiNataliniRicci2004, Generalizations of the Bernoulli and Appell polynomials, Abstr. Appl. Anal. 2004:7 (2004) 613-623, gen>

Carlitz1963b, Products of Appell polynomials, Collect. Math. (1963) Vol. 15, Issue: 3, 245-258, gen>

CostabileLongo2012, Algebraic theory of Appell polynomials with application general linear interpolation problem, Linear Algebra-Theorems and Applications, Edit. by H. A. Yasser, Publ.: InTech, gen>

HassenNguyen2008, Hypergeometric Bernoulli polynomials and Appell sequences, Int. J. Number Theory, Vol. 04, Issue 05, Oct 2008, gen>

HuKim2014, On hypergeometric Bernoulli numbers and polynomials , arXiv (21 Aug 2014), aXv>

KeleshteriMahmudov2015, A q-umbral approach to q-Appell polynomials, arXiv (19 May 2015), aXv>

LiuPanZhang2014, On the integral of the product of the Appell polynomials, Integral Transforms Spec. Funct. Vol.25, Issue 9, 2014, gen>

MaldonadoPradaSenosiain2007, Basic Appell sequences, Taiwanese J. of Math. Vol. 11, No. 4, 1045-1055, 2007, nat>

MaroniMejri2005, Generalized Bernoulli polynomials revisited and some other Appell sequences, Georgian Math. J. Vol. 12 (2005), Number 4, 697-716, nat>

Tempesta2008, On Appell sequences of polynomials of Bernoulli and Euler type, J. Math. Anal. Appl. Vol. 341, Issue 2, May 2008, 1295-1310, nat>

VidŻunas2009, Specialization of Appell’s functions to univariate hypergeometric functions, arXiv(17 Oct 2009), aXv>

array type polynomials

Simsek2013a, Generating function for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications, Fixed Point Theory Appl. 2013, 2013: 87, aXv>

Askey scheme

Ben CheikhLamiriOuni2009, On Askey-scheme and d-orthogonality, I: A characterization theorem, J. Comp. Appl. Math. Vol. 233, Issue 3, 1 Dec 2009, 621-629, jou>

Koornwinder1988, Group theoretic interpretation of Askey's scheme of hypergeometric orthogonal polynomials, Lecture Notes in Math. Vol. 1329, 1988, 46-72, jou>

Koornwinder2005b, Nico Temme, the Askey scheme and me, 1968–2005, published in Liber Amicorum voor Nico Temme, CWI, Amsterdam, 2005, 125-131, gen>

YanallahZahaf2007, New connection formulae for some q-orthogonal polynomials in q-Askey scheme, arXiv (21 Nov 2007), aXv>

Askey-Wilson

GaliffaOng2014, A characterization of an Askey–Wilson difference equation, J. Difference Equ. Appl. Vol. 20, Issue 9, 2014, jou>

IsmailRahman1991, The associated Askey-Wilson polynomials, Trans. Amer. Math. Soc. Vol. 328, No. 1, (Nov 1991), 201-237, nat>

KoelinkStokman1999, The Askey-Wilson function transform scheme, arXiv (23 Dec 1999), aXv>

Koornwinder2007, The structure relation for Askey–Wilson polynomials, J. Comp. Appl. Math. Vol. 207, Issue 2, Oct 2007, 214-226, jou>

Koornwinder2012, Askey-Wilson polynomial, V.2012 Scholarpedia, 7(7): 7761, gen>

VinetZhedanov2008, Generalized Bochner theorem: Characterization of the Askey–Wilson polynomials, J. Comp. Appl. Math. Vol. 211, Issue 1, Jan 2008, 45–56, jou>

Askey-Wilson algebra

Terwilliger2011, The universal Askey-Wilson algebra, SIGMA Symmetry Integrability Geom. Methods Appl. 7 (2011), 069, 24 p, gen>

Barnes-type

Kim D.S.Kim T.2014a, Barnes-type Narumi polynomials, Adv. Difference Equ. 2014, 2014: 182, gen>

Kim D.S.Kim T.KomatsuSeo2014, Barnes-type Daehee polynomials, arXiv (14 Jan 2014), aXv>

 Kim2009b, Barnes type multiple q-zeta functions and q-Euler polynomials, arXiv (28 Dec 2009), aXv>

KimSimsek2005, Barnes’ type multiple Changhee q-zeta functions, arXiv (10 Fev 2005), aXv>

basis

BostanSalvySchost2008, Power series composition and change of basis, arXiv (15 Apr 2008), aXv>

FoataZeilberger1991, Multibasic Eulerian polynomials, Trans. Amer. Math. Soc. Vol. 328, No. 2, (Nov 1991), 843-862, nat>

Ozarslan2013, Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials, Adv. Difference Equations 2013, 2013: 116, gen>

SrivastavaOzarslanYilmaz2014, Some families of differ. equat. assoc. with the Hermite-based Appell polyn. and other classes of Hermite-based polyn., Filomat 28: 4 (2014), 695–708, gen>

Bell

Aigner1999b, A characterization of the Bell numbers, Discrete Math. Vol. 205, Issues 1–3, Jul 1999, 207-210, gen>

BirmajerGilWeiner2015, Linear recurrence sequences and their convolutions via Bell polynomials, J. Integer Seq. Vol. 18 (2015), Article 15.1.2, jis>

Corcino R.B.Corcino C.B.2011, On generalized Bell polynomials, Discrete Dyn. Nat. Soc. Vol. 2011 (2011), Article ID 623456, 21 p, gen>

Corcino R.B.Jaylo-CamposMacodi-Ringia2014, On noncentral Bell numbers and their Hankel transforms, Turkish J. of Analysis and Number Theory 2014, Vol. 2, No. 2, 28-35, nat>

EnnekingAhuja1976, Generalized Bell numbers, Fibonacci Quart. 1976 (14,1):  67-73, fibqy>

Howard1979, Bell polynomials and degenerate Stirling numbers, Rend. Semin. Mat. Univ. Padova, tome 61 (1979), 203-219, nat>

Katriel2008, On a generalized recurrence for Bell  numbers, J. Integer Seq. Vol. 11 (2008), Article 08.3.8, jis>

Katriel2008, On a generalized recurrence for Bell  numbers, J. Integer Seq. Vol. 11 (2008), Article 08.3.8, jis>

LiuWang W.2012, Harmonic number identities via hypergeometric series and Bell polynomials, Integral Transforms Spec. Funct. Vol. 23, Issue 1, 2012, gen>

MansourSchorkShattuck2012, The generalized Stirling and Bell numbers revisited, J. Integer Seq., Vol. 15 (2012), Article 12.8.3, jis>

MansourShattuck2011, A recurrence related to the Bell numbers, Integers 11 (2011), gen>

Mezň2011, The r-Bell numbers, J. Integer Seq. Vol. 14 (2011), Article 11.1.1, jis>

Mezň2012, The dual of Spivey’s Bell number formula, J. Integer Seq. Vol. 15 (2012), Article 12.2.4, jis>

MihoubiBelbachir2014, Linear recurrences for r-Bell polynomials, J. Integer Seq. Vol. 17 (2014), Article 14.10.6, jis>

NataliniRicci2006, Laguerre-type Bell polynomials, Int. J. Math. Math. Sci. Vol. 2006, Article ID 45423, 1-7, gen>

Shallit1980, A triangle for the Bell numbers, Fibonacci Quart.   18th anniversary volume: 69-70, fibqy>

SixdeniersPensonSolomon2001, Extended Bell and Stirling numbers from hypergeometric exponentiation, J. Integer Seq. Vol. 4 (2001), Article 01.1.4, jis>

Spivey2008, A generalized recurrence for Bell numbers, J. Integer Seq. Vol. 11 (2008), Article 08.2.5, jis>

Sun Z-W.Zagi2011, On a curious property of Bell numbers, Bull. Aust. Math. Soc.  84 (2011), no. 1, 153-158, nat>

Wang W.Wang T.2007, Matrices related to the Bell polynomials, Linear Algebra Appl. Vol. 422, Issue 1, Apr 2007, 139-154, gen>

Wang W.Wang T.2008a, Identities via Bell matrix and Fibonacci matrix, Discrete Appl. Math. Vol. 156, Issue 14, 28 Jul 2008, 2793-2803, gen>

Wang W.Wang T.2009, Identities on Bell polynomials and Sheffer sequences, Discrete Math. Vol. 309, Issue 6, 6 Apr 2009, 1637-1648, gen>

Bernoulli

AlexanderZagier1991, The entropy of a certain infinitely convolved Bernoulli measure, J. London Math. Soc. Vol. s2-44, Issue 1 (Aug 1991), 121-134, jou>

AraciAcikgozBagdasaryanSen2013, The Legendre polynomials associated with Bernoulli, Euler, Hermite and Bernstein polynomials, Turkish J. Anal. Number Theory, 2013, Vol. 1, No. 1, 1-3, nat>

Carlitz1954, q-Bernoulli and Eulerian numbers, Trans. Amer. Math. Soc. Vol. 76, No. 2 (Mar 1954), nat>

Cheon G-S.2003, A note on the Bernoulli and Euler polynomials, Appl. Math. Letters Vol. 16, Issue 3, Apr 2003, 365–368, gen>

GouldQuaintance2014, Bernoulli numbers and a new binomial transform identity, J. Integer Seq. Vol. 17 (2014), Article 14.2.2, jis>

Kim2010a, q-Bernstein polynomials, q-Stirling numbers and q-Bernoulli polynomials, arXiv (26 Aug 2010), aXv>

Kim2010b, A note on q-Bernstein polynomials, arXiv (1 Sep 2010), aXv>

KimKimLeeRyoo2010, Some Identities of Bernoulli numbers and polynomials associated with Bernstein polynomials, Adv. Difference Equ. Vol. 2010, Article ID 305018, 7 p, gen>

Bernstein

AraciAcikgozBagdasaryanSen2013, The Legendre polynomials associated with Bernoulli, Euler, Hermite and Bernstein polynomials, Turkish J. Anal. Number Theory, 2013, Vol. 1, No. 1, 1-3, nat>

Cardenas-MoralesGarrancoRasa2011, Bernstein-type operators which preserve polynomials, Comput. Math. Appl. 62 (2011) 158–163, gen>

Kim2010a, q-Bernstein polynomials, q-Stirling numbers and q-Bernoulli polynomials, arXiv (26 Aug 2010), aXv>

Kim2010b, A note on q-Bernstein polynomials, arXiv (1 Sep 2010), aXv>

Kim2013, Some identities on the Bernstein and q-Genocchi polynomials, Bull. Korean Math. Soc. 50 (2013), No. 4, 1289-1296, nat>

KimKimLeeRyoo2010, Some Identities of Bernoulli numbers and polynomials associated with Bernstein polynomials, Adv. Difference Equ. Vol. 2010, Article ID 305018, 7 p, gen>

LavertuLevesque1985, On Bernstein's combinatorial identities, Fibonacci Quart. 1985 (23,4): 347-355, fibqy>

Ostrovska2007, The approximation of logarithmic function by q-Bernstein polynomials in the case q > 1, Numer Algor (Jan 2007) Vol. 44, Issue 1, 69-82, gen>

Simsek2013c, Unification of the Bernstein-type polynomials and their applications, Bound. Value Probl. 2013, 2013: 56, gen>

Veteleanu2010, About q-Bernstein polynomials, Revista Electronică MateInfo.ro Septembrie 2010, gen>

Waldron2005, On the Bernstein–Bézier form of Jacobi polynomials on a simplex, Technical Report-10/14/2005 Dept. of Math., Univ. of Auckland, New Zealand,  nat>

Bessel

Al-JarrahDempseyGlasser2002, Generalized series of Bessel functions, J. Comp. Appl. Math. 143 (2002) 1-8, jou>

Carlitz1964, The coefficients of the reciprocal of a Bessel function, Proc. Amer. Math. Soc. Vol. 15, No. 2 (Apr 1964), 318-320, nat>

ChenIsmailMuttalib1994, Asymptotics of basic Bessel functions and q-Laguerre polynomials, J. Comput. Appl. Math. Vol. 54, Issue 3, Oct 1994, 263-272, jou>

ChenSrivastava1993, A note on certain generating functions for the generalized Bessel polynomials, J. Math. Anal. Appl 180, 151-159 (1993), jou>

CiccoliKoelinkKoornwinder1998, q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations, arXiv (6 May 1998), aXv>

DattoliMiglioratiSrivastava2004, Some families of generating functions for the Bessel and related functions, Georgian Math. J. Vol. 11 (2004), No. 2, 219-228, nat>

Dhaouadi2013, On the q-Bessel Fourier transform, Bull. Math. Anal. Appl. Vol. 5 Issue 2 (2013), 42-60, nat>

Kar1996, On a general class of generating functions involving modified Bessel

 polynomials, Bulletin Calcutta Math. Soc. Vol. 88, No. 5, Oct 1996, Article No. 51, 363-366, nat>

LinChenSrivastava2003, Certain classes of finite-series relationships and generating Bessel polynomials, Appl. Math. Comput. Vol. 137, Issues 2–3, 25 May 2003, 261-275, gen>

PatilThakare1976b, Some generating functions in unified form for the classical orthogonal polynomials and Bessel polynomials, Indian J. Pure Appl. Math. 1976 (8,1):  94-102, nat>

PurohitKalla2007, On q-Laplace transforms of the q-Bessel functions, Fract. Calc.       Appl. Anal. Vol. 10, No. 2, (2007), 189-196, gen>

Yang S-l.Zheng2013a, A determinant expression for the generalized Bessel polynomials, J. of Applied Math. Vol. 2013 (2013), Article ID 242815, 6 p, jou>

Bessel big q-analogues

CiccoliKoelinkKoornwinder1998, q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations, arXiv (6 May 1998), aXv>

Binet formula

BernoussiMottaRachidiSaeki2001, Approximation of infinite generalized Fibonacci sequences and their asymptotic Binet formula, Fibonacci Quart. 2001 (39,2): 168-180, fibqy>

Brousseau1969a, Linear recursion relations Lesson Three -- The Binet formulas, Fibonacci Quart. 1969 (7,1): 99-104, fibqy>

DresdenDu2014, A simplified Binet formula for k-generalized Fibonacci numbers, J. Integer Seq. Vol. 17 (2014), Article 14.4.7, jis>

EdsonYayenie2009, A new generalization of Fibonacci sequence and extended Binet's formula, Integers 9 (2009), 639-654, gen>

KappraffAdamson2004, Generalized Binet formulas, Lucas polynomials, and cyclic constants, Forma 19, 355-366, 2004, gen>

Kiliç2008, The Binet formula, sums and representations of generalized Fibonacci p-numbers, European J. Combin. Vol. 29, Issue 3, Apr 2008, 701-711, gen>

KiliçTasci2006, The generalized Binet formula, representation and sums of the generalized order-k Pell numbers, Taiwanese J. of Math. Vol. 10, No. 6, 1661-1670, Dec 2006, nat>

LeeLeeKimShin2001, The Binet formula and representations of k-generalized Fibonacci numbers, Fibonacci Quart. 2001 (39,2): 158-164, fibqy>

Mahajan2014, The Binet forms for the Fibonacci and Lucas numbers, Int. J. of Math. Trends and Technology Vol.10, No. 1, Jun 2014, gen>

StakhovRozin2006, Theory of Binet formulas for Fibonacci and Lucas p-numbers, Chaos, Soliton and Fractals, Vol. 27, Issue 5, Mar 2006, 1162-1177, gen>

binomial

Amghibech2007, On sums involving binomial coefficients, J. Integer Seq. Vol. 10 (2007), Article 07.2.1, jis> gen>

Andrews1990, Euler's "Exemplum Memorabile Induction Fallacis" and q-trinomial coefficients, J. Amer. Math. Soc. Vol. 3, No. 3, Jul 1990, nat>

Azarian2012a, Fibonacci identities as binomial sums, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 38, 1871-1876, gen>

Azarian2012b, Fibonacci identities as binomial sums II, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 42, 2053-2059, gen>

Azarian2012c, Identities involving Lucas or Fibonacci and Lucas numbers as binomial sums, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 45, 2221-2227, gen>

BelbachirMihoubi2015, The (exponential) multipartitional polynomials and polynomial sequences of multinomial type, Part II, Arab J. Math. Sci. Vol. 21, Issue 1, Jan 2015, 2-14, nat>

BelbachirRahmaniSury2011, Sums involving moments of reciprocals of binomial coefficients, J. Integer Seq. Vol. 14 (2011), Article 11.6.6, jis>

BelbachirRahmaniSury2012, Alternating sums of the reciprocals of binomial coefficients, J. Integer Seq. Vol. 15 (2012), Article 12.2.8, jis>

BenjaminRouse2004, Recounting binomial Fibonacci identities, Proc. of the 10th Int. Conf. on Fibonacci nbs. and their Appl. 2004, Vol. 9, 25-28, gen>

Benoumhani2003, A sequence of binomial coefficients related to Lucas and Fibonacci numbers, J. Integer Seq. Vol. 6 (2003), Article 03.2.1, jis>

BensonRatcliff2009, Combinatorial properties of generalized binomial coefficients, Contemp. Math. 2009, vol. 491, 141-150, gen>

Boyadzhiev2012, Series with central binomial coefficients, Catalan numbers, and harmonic numbers, J. Integer Seq. Vol. 15 (2012), Article 12.1.7, jis>

Carlitz1976a, Some binomial sums, Fibonacci Quart. 1976 (14,3): 249-253, fibqy>

Carlitz1976b, Some sums of multinomial coefficients, Fibonacci Quart. 1976 (14,5):  427-438, fibqy>

Cooper2013, The q-binomial theorem, Auckland Mathematical Association, HoD Day, 17 May 2013, nat>

Duarte, de Oliveira2013, Note on the convolution of binomial coefficients, J. Integer Seq. Vol. 16 (2013), Article 13.7.6, jis>

Dzhumadil'daevYeliussizov2013, Power sums of binomial coefficients, J. Integer Seq. Vol. 16 (2013), Article 13.1.4, jis>

Elsner2005, On recurrence formulae for sums involving binomial coefficients, Fibonacci Quart. 2005 (43,1):  31-45, fibqy>

Gould1967, The Bracket function, q-binomial coefficients, and some new Stirling number formulas, Fibonacci Quart. 1967 (5,5):  401-423, fibqy>

Gould1974, The design of the four binomial identities: Moriarty intervenes, Fibonacci Quart. 1974 (12,3): 300-308, fibqy>

GouldQuaintance2014, Bernoulli numbers and a new binomial transform identity, J. Integer Seq. Vol. 17 (2014), Article 14.2.2,  jis>

Hodel1974, Combinatorial interpretation of an analog of generalized binomial coefficients, Fibonacci Quart. 1974 (12,4):  360-362, fibqy>

Hoggatt, Jr.1967, Fibonacci numbers and generalized binomial coefficients, Fibonacci Quart. 1967 (5,4):  383, fibqy>

JouhetLassZeng2003, Sur une généralisation des coefficients binomiaux, arXiv (3 Mar 2003),  aXv>

KyriakoussisVamvakari2007, Asymptotic behaviour of a q-binomial type distribution based on q-Krawtchouk orthogonal polynomials, J. Comput. Anal. Appl. Vol. 8, No. 1, 2007, jou>

Loeb1992, A generalization of the binomial coefficients, Discrete Math. Vol. 105, Issues 1–3, 14 Aug 1992, 143-156, gen>

MihoubiMaamra2011, Touchard polynomials, partial Bell polynomials and polynomials of binomial type, J. Integer Seq. Vol. 14 (2011), Article 11.3.1, jis>

Nguyen2013, Generalized binomial expansions and Bernoulli polynomials, Integers 13 (2013), gen>

Roman1992, The logarithmic binomial formula, Amer. Math. Monthly, Vol. 99, No. 7 (Aug. - Sep., 1992), 641-648,  nat>

RotaShenTaylor1997, All polynomials of binomial type are represented by Abel polynomials, Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 25.3-4 (1997):  731-738, nat>

Sofo2008a, Double sums of binomial coefficients, Int. Math. Forum, 3, 2008, no. 31, 1501-1512, gen>

Sofo2008b, Sums of reciprocals of triple binomial coefficients, Int. J. Math. Math. Sci. Vol. 2008, Article ID 794181, 11 p, gen>

Sofo2011b, Integral identities for rational series involving binomial coefficients, Bull. Malays. Math. Sci. Soc. (2) 34(3) (2011), 631–637, nat>

SpiveySteil2006, The k-binomial transforms and the Hankel transform, J. Integer Seq. Vol. 9 (2006), Article 06.1.1, jis>

Stam1988, Polynomials of binomial type and compound Poisson processes, J. Math. Anal. Appl. Vol. 130, Issue 2, Mar 1988, 493-08, jou>

Strehl1994, Binomial identities -- combinatorial and algorithmic aspects, Discrete Math. Vol. 136, Issues 1–3, 31 Dec1994, 309-346,  gen>

Sun Z-H.2001a, Invariant sequences under binomial transformation, Fibonacci Quart. 2001 (39,4):  324-333, fibqy>

Sun Z-W.2002, On the sum sigma(k=r)(mod m) binomial(n,k) and related congruences, Israel J. Math. 128 (2002), 135-156, nat>

Sun Z-W.2010b, Binomial coefficients, Catalan numbers and Lucas quotients, Sci. China Math. 53 (2010), no. 9, 2473-2488, nat>

Sun Z-W.Tauraso2007, Congruences for sums of binomial coefficients, J. Number Theory, Vol. 126, Issue 2, Oct 2007, 287-296, jou>

Sun Z-W.Tauraso2011, On some new congruences for binomial coefficients, Int. J. Number Theory, 07 (2011), No. 3, 645-662, gen>

Szablowski2014, A few remarks on Euler and Bernoulli polyn. and their connections with binom. coef. and modifi…ed Pascal matrices, Math. Ćterna, Vol. 4, 2014, no. 1, 83-88, gen>

Trif2000, Combinatorial sums and series involving inverses of binomial coefficients, Fibonacci Quart. 2000 (38,1): 79-83, fibqy>

Wang Yi2005, Self-inverse sequences related to a binomial inverse pair, Fibonacci Quart. 2005 (vol.43 ,1): 46-52, fibqy>

Yang J-H.Zhao2006, Sums involving the inverses of binomial coefficients, J. Integer Seq. Vol. 9 (2006), Article 06.4.2, jis>

Brownian motion, Brownian motion q-analogue

AbateWhitt2011, Brownian Motion and the generalized Catalan numbers, J. Integer Seq. Vol. 14 (2011), Article 11.2.6, jis>

BassoNardon, Brownian motion, Dept. of Applied Mathematics University Ca’ Foscari Venice, nat>

BianePitmanYor2001, Probability laws related to the Jacobi theta and Rieman z functions, and Brownian motion excursions, Bull. Amer. Math. Soc. (N.S.) Vol. 38, no. 4, 435-465, nat>

Bryc2014, On integration with respect to the q-Brownian motion, Statist. Probab. Lett. 94 (2014) 257-266, gen>

Herzog2013, Brownian motion and Poisson process, Stochastische Systeme, 2013, gen>

Catalan

AbateWhitt2011, Brownian Motion and the generalized Catalan numbers, J. Integer Seq. Vol. 14 (2011), Article 11.2.6, jis>

Bouras2013, A new characterization of Catalan numbers related to Hankel transforms and Fibonacci numbers, J. Integer Seq. Vol. 16 (2013), Article 13.3.3, jis>

Boyadzhiev2012, Series with central binomial coefficients, Catalan numbers, and harmonic numbers, J. Integer Seq. Vol. 15 (2012), Article 12.1.7, jis>

Callan2005, A combinatorial interpretation for a super-Catalan recurrence, J. Integer Seq. Vol. 8 (2005), Article 05.1.8, jis>

Cigler2013, Some remarks about q-Chebyshev polynomials and q-Catalan numbers and related results, arXiv (? 2013), aXv>

Elezovic2014, Asymptotic expansions of central binomial coefficients and Catalan numbers, J. Integer Seq. Vol. 17 (2014), Article 14.2.1, jis>

NkwantaBarnes2012, Two Catalan-type Riordan arrays and their connections to the Chebyshev polyn. of the first kind, J. Integer Seq. Vol. 15 (2012), Article 12.3.3, jis>

NkwantaTefera2013, Curious relations and identities involving the Catalan generating function and numbers, J. of Integer Seq. Vol. 16 (2013), Article 13.9.5, jis>

Rogers1978, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math. Vol. 22, Issue 3, 1978, 301–310, gen>

Sun Z-W.2010b, Binomial coefficients, Catalan numbers and Lucas quotients, Sci. China Math. 53 (2010), no. 9, 2473–2488, nat>

Cauchy

BertolaGekhtmanSzmigielski2010, Cauchy biorthogonal polynomials, J. Approx. Theory Vol. 162, Issue 4, Apr 2010, 832-867, jou>

CandelpergherCoppo2012, A new class of identities involving Cauchy numbers, harmonic numbers and zeta values, Ramanujan J. April 2012, Volume 27, Issue 3, 305-328, gen>

KamanoKomatsu2013, Poly-Cauchy polynomials, Moscow J. of Combin. and Number Theory 2013, Vol. 3, Issue 2,  61-87 [181-207], nat>

KimKim2013c, Higher -order Cauchy of the first kind and poly-Cauchy of the first kind mixed type polynomials, arXix (9 Aug 2013), aXv>

KimKim2013e, Poisson-Charlier and poly-Cauchy mixed-type polynomials, arXix (4 Sep 2013), aXv>

KimKim2013g, Higher-order Cauchy numbers and polynomials, arXiv (12 Oct 2013), aXv>

Komatsu2013a, Poly-Cauchy numbers, Kyushu J. Math. 67 (2013), 143-153, nat>

Komatsu2013b, Sums of products of Cauchy numbers, including poly-Cauchy numbers, J. Discrete Math. Vol, 2013 (2013), Article ID 373927, 10 p, jou>

Komatsu2013c, Poly-Cauchy numbers and poly-Bernoulli numbers, xxxx, xxxx>

KomatsuLaohakosolLiptal2013, A generalization of poly-Cauchy numbers and their properties, Abstr. Appl. Anal. Vol. 2013 (2013), Article ID 179841, 8 p,  gen>

KomatsuLuca2013, Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers, Ann. Math. Inform. 41 (2013) 99-105,  gen>

LiuQiDing2010, Some recurrence relations for Cauchy numbers of the first kind, J. Integer Seq. Vol. 13 (2010), Article 10.3.8, jis>

MerliniSprugnoliVerri2006, The Cauchy numbers, Discrete Math. Vol. 306, Issue 16, Aug 2006, 1906-1920, gen>

central coefficients

Barry2013a, On the central coefficients of Riordan matrices, J. Integer Seq. Vol. 16 (2013), Article 13.5.1, jis>

BlasiakDattoliHorzelaPensonZhukovsky2008, Motzkin numbers, central trinomial coefficients and hybrid polyn., J. Integer Seq. Vol. 11 (2008), Article 08.1.1, jis>

Boyadzhiev2012, Series with central binomial coefficients, Catalan numbers, and harmonic numbers, J. Integer Seq. Vol. 15 (2012), Article 12.1.7, jis>

Elezovic2014, Asymptotic expansions of central binomial coefficients and Catalan numbers, J. Integer Seq. Vol. 17 (2014), Article 14.2.1, jis>

GuoZeng2012, New congruences for sums involving Apéry numbers or central Delannoy numbers, arXiv (25 May 2012), aXv>

Hetyei2006a, Central Delannoy numbers and balanced Cohen-Macaulay complexes, Ann. Comb. 10 (2006) 443-462,  gen>

Hetyei2006b, Central Delannoy numbers, Legendre polynomials, and a balanced join operation preserving the Cohen-Macaulay property, Formal Power Series and Algebraic Combinatorics-San Diego, California 2006, gen>

Kruchinin D.Kruchinin V.2012, A method for obtaining generating functions for central coefficients of triangles, J. Integer Seq., Vol. 15 (2012), Article 12.9.3, jis>

Mikic2016, A Proof of a Famous Identity Concerning the Convolution of the Central Binomial Coefficients, J. Integer Seq. Vol. 19 (2016), Article 16.6.6, jis>

Noe2006, On the divisibility of generalized central trinomial coefficients, J. of Integer Seq., Vol. 9 (2006), Article 06.2.7, jis>

PetkovicRajkovicBarry2011, The Hankel transform of generalized central trinomial coefficients and related sequences, Integral Transforms Spec. Funct. 2011 (vol.22,1):  29-44, gen>

Robbins1987, Representing binom (2n n) as a sum of squares, Fibonacci Quart. 1987 (25,1): 29-33,  fibqy>

Romik2003, Some formulas for the central trinomial and Motzkin number, J. Integer Seq. Vol. 6 (2003), Article 03.2.4, jis>

Sprugnoli2006, Sums of reciprocals of the central binomial coefficients, Integers 6 (2006), gen>

Sprugnoli2012, Alternating weighted sums of inverses of binomial coefficients, J. Integer Seq. Vol. 15 (2012), Article 12.6.3, jis>

Sulanke2003, Objects counted by the central Delannoy numbers, J. Integer Seq. Vol. 6 (2003), Article 03.1.5,  jis>

Sun Z-W.2010a, On Apéry numbers and generalized central trinomial coefficients, arXiv (19 Aug 2010), aXv>

Sun Z-W.2011c, On congruences related to central binomial coefficients, J. Number Theory, 131 (2011), no. 11, 2219-2238, jou>

Sun Z-W.2014, Congruences involving generalized central trinomial coefficients, Sci. China Math. 2014, Vol. 57, Issue 7, 1375-1400, nat>

central factorial numbers

Charalambides1981, Central factorial numbers and related expansions, Fibonacci Quart. 1981 (19,5): 451-455, fibqy>

KangRyoo2013, A research on a certain family of numbers and polynomials related to Stirling numbers, central factorial numbers, and Euler numbers, J. Appl. Math. Vol. 2013 (2013), Article ID 158130, 10 p, jou>

Chan-Chyan-Srivastava

SrivastavaNisarKhan2014, Some umbral calculus presentations of the Chan-Chyan-Srivastava polyn. and the Erkus-Srivastava polyn., Proyecciones, Vol. 33, No 1, 77-90, Mar 2014, gen>

Charlier

de MedicisStantonWhite1995, The combinatorics of q-Charlier polynomials, J. Comb. Theory Ser. A, Vol. 69, Issue 1, Jan 1995, 87-114, jou>

KimStantonZeng2006, The combinatorics of the Al-Salam-Chihara q-Charlier polynomials, Sém. Lothar. Combin 54 (2006), Article B54i, gen>

Shibukawa2014, Multivariate Meixner, Charlier and Krawtchouk polynomials, arXiv (29 Apr 2014), aXv>

Zeng J.1995, The q-Stirling numbers, continued fractions and the q-Charlier and q-Laguerre polyn., J. Comp. Appl. Math. Vol. 57, Issue 3, Feb 1995, 413-424, aXv>

Chebyshev (Tschebyscheff)

AharonovBeardonDriver2005, Fibonacci, Chebyshev, and orthogonal polynomials, Amer. Math. Monthly Vol. 112, No. 7 (2005), 612-630, nat>

Barry2009c, Symmetric third-order recurring sequences, Chebyshev polynomials, and Riordan arrays, J. Integer Seq. Vol. 12 (2009), Article 09.8.6, jis>

BenjaminEricksenJayawantShattuck2010, Combinatorial trigonometry with Chebyshev polynomials, J. Statist. Plann. Inference, Vol. 140, Issue 8, Aug 2010, 2157-2160, jou>

BenjaminWalton2009, Counting on Chebyshev polynomials, Mathematics Magazine, Vol. 82, No. 2, 117-126. Apr 2009, gen>

BenjaminWalton2010, Combinatorially composing Chebyshev polynomials, J. Statist. Plann. Inference, Vol. 140, Issue 8, Aug 2010, 2161-2167, jou>

BergumWagnerHoggatt, Jr.1975, Chebeyshev polynomials and related sequences, Fibonacci Quart. 1975 (13,1): 19-24, fibqy>

BoyadjievScherer2001, On the Chebyshev polynomials, Kuwait J. Sci. Eng. 28(2) 2001, nat>

Buschman1963, Fibonacci numbers, Chebyshev polynomials, generalizations and difference equations, Fibonacci Quart. 1963 (1,4): 1-7,  fibqy>

ChenGriffinIsmail2007, Generalizations of Chebyshev polynomials and polynomial mappings, Trans. Amer. Math. Soc. Vol. 359, No. 10, Oct 2007, 4787-4828, nat>

ChenMansourZou2012, Embedding distributions and Chebyshev polynomials, Graphs and Combinatorics Vol. 28, Issue 5 , 597-614, gen>

Cigler2013, Some remarks about q-Chebyshev polynomials and q-Catalan numbers and related results, arXiv (? 2013), aXv>

Dragomir2014, Approximating the Riemann-Stieltjes integral via a Chebyshev type functional, Acta Comment. Univ. Tartu. Math. Vol. 18, Number 2, 2014, nat>

Egge2007, Restricted colored permutations and Chebyshev polynomials, Discrete Math. Vol. 307, Issue 14, 28 Jun 2007, 1792-1800, gen>

ElizaldeMansour2005, Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials, Discrete Math. 305 (2005) 170-189, gen>

FaberLiesenTichy2010, On Chebyshes polynomials of matrices, SIAM J. Matrix Anal. Appl. 2010, gen>

GoginHirvensalo2007, On the generating function of discrete Chebyshev polynomials, Turku Centre for Computer Science, TUCS Technical Report No 819, Apr 2007, nat>

Horadam1969, Tschebyscheff and other functions associated with the sequence {Wn(a,b;p,q)}, Fibonacci Quart. 1969 (7,1): 14-22, fibqy>

Jaiswal1974, On polynomials related to Tchebichef polynomials of the second kind, Fibonacci Quart. 1974 (12,3): 263-264, fibqy>

Kimberling1980a, Mixing properties of mixed Chebyshev polynomials, Fibonacci Quart. 1980 (18,4): 332-340, fibqy>

Kimberling1980b, Four composition identities for Chebyshev polynomials, Fibonacci Quart. 1980 (18,4): 353-369, fibqy>

KimKimLee2014, Some identities for Bernoulli polynomials involving Chebyshev polynomials, J. Comput. Anal. Appl. Jan 2014, Vol. 16, Issue 1, 172, jou>

KimZeng2003, Combinatorics of generalized Tchebycheff polynomials, European J. Combin. Vol. 24, Issue 5, Jul 2003, 499-509, gen>

KitaevMansour2005, Linear recurrences and Chebyshev polynomials, Fibonacci Quart. 2005 (43,3): 256-261, fibqy>

Kuijlaars1995, Chebyshev-type quadrature and zeros of Faber polynomials, J. Comput. Appl. Math. Vol. 62, Issue 2, Sep 1995, 155-179, jou>

Lang1992, A combinatorial problem in the Fibonacci nb. system and two-variable generalizazions of Chebyshev's polyn., Fibonacci Quart. 1992 (30,3): 199-210,  fibqy>

LeeWong2011, On Chebyshev's polynomials and certain combinatorial identities, Bull. Malays. Math. Sci. Soc. (2) 34(2) (2011), 279-286, nat>

Li2014, On Chebyshev polynomials, Fibonacci polynomials, and their derivatives, J. Appl. Math. Vol. 2014, Article ID 451953, 8 p, jou>

MansourVainshtein2000, Restricted permutations, continued fractions, and Chebyshev polynomials, Electron. J. Combin. 7 (2000), #R17, gen>

MansourVainshtein2002, Restricted permutations and Chebyshev polynomials, Sém. Lothar. Combin. 47 (2002), Article B47c, gen>

MelhamShannon1995c, On reciprocal sums of Chebyshev related sequences, Fibonacci Quart. 1995 (33,3): 194-202, fibqy>

NkwantaBarnes2012, Two Catalan-type Riordan arrays and their connections to the Chebyshev polyn. of the first kind, J. Integer Seq. Vol. 15 (2012), Article 12.3.3, jis>

Pethe1985, On Lucas fundamental functions and Chebychev polynomial sequences, Fibonacci Quart. 1985 (23,1): 57-65, fibqy>

Stankov2013, On linear combinations of Chebyshev polynomials, arXiv (9 Nov 2013), aXv>

Zhang W.2002, On Chebyshev polynomials and Fibonacci numbers, Fibonacci Quart. 2002 (40,5):  424-428, fibqy>

Chebyshev-Boubaker

Barry2013d, On the connection coefficients of the Chebyshev-Boubaker polynomials, The Scientific World J. Vol. 2013 (2013), Article ID 657806, 10 p, gen>

circulant matrices

BottcherGrudskyArellano2004, Approximating inverses of Toeplitz matrices by circulant matrices, Methods Appl. Anal. Vol. 11, No. 2, p 211-220, Jun 2004,  gen>

CarliFerrantePavonPicci2013, An efficient algorithm for maximum entropy extension of block-circulant covariance matrices, Linear Algebra Appl. Vol. 439, Issue 8, 15 Oct 2013, 2309–2329 arXiv (8 Feb 2013), aXv>

CivcivTurkmen2007, Notes on norms of circulant matrices with Lucas number, Int. J. of Information and Systems Sc. Vol. 4, Number 1, P 142-147, gen>

GellerKraPopescuSimanca2012, On circulant matrices, Preprint, gen>

KraSimanca2012, On circulant matrices, Notices AMS, Vol. 59, Number 3, 2012, nat>

Tee2007, Eigenvectors of block circulant and alternating circulant matrices, New Zealand J. Math. Vol. 36 (2007), 195-211, nat>

Varga1954, Eigenvalues of circulant matrices, Pacific J. Math. Vol. 4, No. 1 May 1954, nat>

Zellini1979, On some properties of circulant matrices, Linear Algebra Appl 26:31-43(1979), gen>

ZelliniMack1981, On some theorems on circulant matrices, Linear Algebra Appl. Vol. 41, Dec 1981, 137-149, gen>

coefficients method

 EhrenborgReaddy2016, The Gaussian coefficient revisited, J. Integer Seq. Vol. 19 (2016), Article 16.7.8, jis>

MerliniSprugnoliVerri2007, The method of coefficients, Amer. Math. Monthly, Vol. 114, No. 1 (Jan., 2007), 40-57, nat>

Szwarc1992, Connection coefficients of orthogonal polynomials, Canad. Math. Bull. Vol. 35 (4), 1992, 548-556, nat>

Cohen-Macaulay property

Hetyei2006a, Central Delannoy numbers and balanced Cohen-Macaulay complexes, Ann. Comb. 10 (2006) 443-462,  gen>

Hetyei2006b, Central Delannoy numbers, Legendre polynomials, and a balanced join operation preserving the Cohen-Macaulay property, Formal Power Series and Algebraic Combinatorics-San Diego, California 2006, gen>

combinatorial theory

AkyuzHalici2013, On some combinatorial identities involving the terms of generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat. Vol. 42 (4) (2013), 431-435,  gen>

AndersonBenjaminRouse2005, Combinatorial proofs of Fermat's, Lucas's, and Wilson's theorems, Amer. Math. Monthly, Vol. 112, No. 3, 266-268, Mar 2005, nat>

AndradeSantosdaSilvaSilva2013, Polyn. generalizations and combin. interpretations for seq. including the Fibonacci and Pell numbers, Open J. Discrete Math. 2013, 3, 25-32, gen>

BelbachirBelkhirBousbaa2014, Combinatorial approach of certain generalized Stirling numbers, arXiv (23 Nov 2014), aXv>

BelbachirBousbaa2014b, Combinatorial identities for the r-Lah numbers, Ars Comb. 115:  453-458 (2014),  gen>

BelbachirKomatsuSzalay2014, Linear recurrences associated to rays in Pascal's triangle and combinatorial identities, Math. Slovaca 64 (2014), No. 2, 287-300, nat>

Belbahri2010, Scale invariant operators and combinatorial expansions, Adv. in Appl. Math. Vol. 45, Issue 4, Oct 2010, 548-563, gen>

BenjaminCameronQuinn2007, Fibonacci deteminants - a combinatorial approach, Fibonacci Quart. 45(1): 39-55. Claremont Colleges - HMC Faculty Scholarship, fibqy>

BenjaminDresden2007, A combinatorial proof of Vandermonde's determinant, Amer. Math. Monthly, Vol. 114, No. 4, 338-341, Apr 2007, nat>

BenjaminEricksenJayawantShattuck2010, Combinatorial trigonometry with Chebyshev polynomials, J. Statist. Plann. Inference, Vol. 140, Issue 8, Aug 2010, 2157–2160, jou>

BenjaminPlott2008-2009, A combinatorial approach to fibonomial coefficients, Fibonacci Quart. 2008-09 (46-47,1): 7-9, fibqy>

BenjaminWalton2010, Combinatorially composing Chebyshev polynomials, J. Statist. Plann. Inference, Vol. 140, Issue 8, Aug 2010, 2161-2167, jou>

BensonRatcliff2009, Combinatorial properties of generalized binomial coefficients, Contemp. Math. 2009, vol. 491, 141-150, gen>

BergumHoggatt, Jr.1978, A combinatorial problem involving recursive sequences and tridiagonal matrices, Fibonacci Quart. 1978 (16,2): 113-117,  fibqy>

Brietzke2008, An identity of Andrews and a new method for the Rordan array proof of combinatorial identities, Discrete Math. Vol. 308, Issue 18, Sep 2008, 4246-4262, gen>

CakicEl-DesoukyMilovanovic2013, Explicit formulas and combinatorial identities for generalized Stirling numbers, Mediterr. J. Math. Feb 2013, Vol. 10, Issue 1, 57-72, nat>

Callan2005, A combinatorial interpretation for a super-Catalan recurrence, J. Integer Seq. Vol. 8 (2005), Article 05.1.8, jis>

Cameron2011, Combinatorics with the Riordan Group, NUMS Conference Reed College, Apr 9, 2011, gen>

Cameron2013, Enumerative combinatorics 5: q-analogues, The LTCC lectures, Autumn 2013, gen>

CanDagli2014, Extended Bernoulli and Stirling matrices and related combinatorial identities, Linear Algebra Appl. Vol. 444, Mar 2014, 114-131 arXiv(4 Dec 2013), aXv>

CheonKimShapiro2012, Combinatorics of Riordan arrays with identical A and Z sequences, Discrete Math. Vol. 312, Issues 12–13, Jul 2012, 2040-2049, gen>

Chu1994a, Inversion techniques and combinatorial identities. - A unified treatment for the 7F6–series identities, Collect. Math. 45, 1 (1994), 13–43, gen>

Chu1994b, Inversion techniques and combinatorial identities. Strange evaluations of basic hypergeometric series, Compos. Math. tome 91, no 2 (1994), 121-144, gen>

Chu1995, Inversion techniques and combinatorial identities. Jackson’s q-analogue of the Dougall-Dixon theorem and the dual formulae, Compos. Math. 95:  43-68, 1995, gen>

Chu2002, Inversion techniques and combinatorial identities: balanced hypergeometric series, Rocky Mountain J. Math. Vol. 32, No. 2 (2002), 561-588, nat>

ClarkeHanZen1997, A combinatorial interpretation of the Seidel generation of q-derangement numbers, Annals Comb. 1997, Vol. 1, Issue 1, 313-327, gen>

CohnEvenMengerHooper1962, On the number of partitionings of a set of n distinct objects, Amer. Math. Monthly, Vol. 69, No. 8 (Oct 1962), 782-785, nat>

Corcino R.B.Fernandez2014, A combinatorial approach for q-analogue of r-Stirling Numbers, British J. of Math. and Computer Sci. BJMCS 4 (9), 1268-1279, 2014, nat>

Huang1997, Applications of residues to combinatorial identities, Proc. Amer. Math. Soc. 125 (1997), 1011-1017, nat>

Kemeny1984, Matrix representation for combinatorics, J. Combin. Theory Ser. A, Vol. 36, Issue 3, May 1984, 279–306, jou>

KimStantonZeng2006, The combinatorics of the Al-Salam-Chihara q-Charlier polynomials, Sém. Lothar. Combin 54 (2006), Article B54i, gen>

KimZeng2003, Combinatorics of generalized Tchebycheff polynomials, European J. Combin. Vol. 24, Issue 5, Jul 2003, 499-509, gen>

Lang2009, Combinatorial interpretation of generalized Stirling numbers, J. Integer Seq. Vol. 12 (2009), Article 09.3.3, jis>

MezňDil2009, Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence, Cent. Eur. J. Math. Jun 2009, Vol. 7, Issue 2, 310-321, gen>

Riordan1964, Inverse relations and combinatorial identities, Amer. Math. Monthly vol.71, No. 5 (May, 1964), 485-498, nat>

Rota1996, Report on the present state of combinatorics, Discrete Math. 153 (1996), 289-303, gen>

RotaKahanerOdlyzko1973, On the foundations of combinatorial theory. VIII. Finite operator calculus, J. Math. Anal. Appl. Vol. 42, Issue 3, Jun 1973, 684-760, jou>

ShannonOllerton2002, Combinatorial matrices and linear recursive sequences, Fibonacci Quart. 2002 (40,5):  417-423, fibqy>

Spivey2011, On solutions to a general combinatorial recurrence, J. Integer Seq. Vol. 14 (2011), Article 11.9.7, jis>

Strehl1994, Binomial identities -- combinatorial and algorithmic aspects, Discrete Math. Vol. 136, Issues 1–3, 31 Dec1994, 309-346, gen>

Sun Z-W.2003a, Combinatorial identities in dual sequences, Europ. J. Combin. 24 (2003), 709-718, gen>

Sun Z-W.2007, Combinatorial congruences and Stirling numbers, Acta Arith. 126 (2007), no. 4, 387-398, gen>

Trif2000, Combinatorial sums and series involving inverses of binomial coefficients, Fibonacci Quart. 2000 (38,1): 79-83, fibqy>

Viennot1983, Une théorie combinatoire des polynômes orthogonaux généraux, Notes de conférences données ŕ l’Univ. du Québec ŕ Montréal, gen>

Wang Yi.Zhang Z-H.2015, Combinatorics of generalized Motzkin numbers, J. Integer Seq. Vol. 18 (2015), Article 15.2.4, jis>

Webster1995, A combinatorial problem with a Fibonacci solution, Fibonacci Quart. 1995 (33,1): 26-31, fibqy>

XiongHallTsao2014, Combinatorial interpretation of general Eulerian numbers, J. Discrete Math. Vol. 2014 (2014), Article ID 870596, 6 p, jou>

ZhangWuyungaowaMa2013, A class of formal operators for combinatorial identities and its application, Int. J. of Mathematical, Comput., Physical and Quantum Engineer. Vol. 7, No:3, 2013, gen>

Comtet

El-DesoukyGomaa2011, q-Comtet and generalized q-harmonic numbers, J. Math. Sci .Adv. Appl. Vol. 10, Number 1/2, 2011, 33-52, jou>

congruences

Adelberg1998, 2-adic congruences of Nörlund numbers and of Bernoulli numbers of the second kind, J. Number Theory 73, 47-58 (1998), jou>

Adelberg2000, Universal higher order Bernoulli numbers and Kummer and related congruences, J. Number Theory Vol. 84, Issue 1, Sep 2000, 119-135, jou>

Adelberg2004, Universal Bernoulli polynomials and p-adic congruences, Proc. of the 10th Int. Conf. on Fibonacci nbs. and their Appl. 2004, Vol. 9, 1-8, gen>

Ballot2014, On a congruence of Kimball and Webb involving Lucas sequences, J. Integer Seq. Vol. 17 (2014), Article 14.1.3, jis>

CenkciKurt2008, Congruences for generalized q-Bernoulli polynomials, J. Inequal. Appl. Vol. 2008, Article ID 270713, 19 p, jou>

ChanManna2010, Congruences for Stirling numbers of the second kind, Contemporary Math.-Gems in Experimental Math. Vol. 517, 97-11, gen>

Chen2004, Congruences for Euler numbers, Fibonacci Quart. 2004 (42,2):  128-140, fibqy>

Dilcher2008, Determinant expressions for q-harmonic congruences and degenerate Bernoulli numbers, Electron. J. Combin. 15 (2008), gen>

Ieronymou2014, Congruences involving sums of ratios of Lucas sequences, J. Integer Seq. Vol. 17 (2014), Article 14.8.8, jis>

Liu2001, Identities and congruences involving higher-order Euler-Bernoulli numbers and polynomials, Fibonacci Quart. 2001 (39,3):  279-284, fibqy

Liu2006, Congruences for higher-order Euler numbers, Proc. Japan Acad. 82, Series A, (2006), No. 3, 30-33, nat>

NymannSaenz1999, Eulerian numbers: inversion formulas and congruences modulo a prime, Fibonacci Quart. 1999 (37,2): 154-161, fibqy>

Pilehrood Kh.Pilehrood T.Tauraso2012, Congruences concerning Jacobi polynomials and Apéry polynomials and Apéry-like formulae, Int. J. Number Theory, 8 (2012), no. 7, 1789–1811, gen>

Sburlati2002, Generalized Fibonacci sequences and linear congruences, Fibonacci Quart. 2002 (40,5):  446-452, fibqy>

ShannonCookHillman2013, Some aspects of Fibonacci polynomial congruences, Ann. Math. Inform. 41 (2013), 211–217 Proc. of the 15th Int. Conf. on Fib. nbs. and their Appl., gen>

ShannonHoradamCollings1974, Some congruences for Fibonacci numbers, Fibonacci Quart. 1974 (12,4): 351-354,  fibqy>

Sun Z-H.2008, Congruences involving Bernoulli polynomials, Discrete Math Vol. 308, Issue 1, 6 Jan 2008, 71-112,  gen>

Sun Z-W.2002, On the sum sigma(k=r)(mod m) binomial(n,k) and related congruences, Israel J. Math. 128 (2002), 135-156,  nat>

Sun Z-W.2003b, General congruences for Bernoulli polynomials, Discrete Math. 262 (2003), 253-276, gen>

Sun Z-W.2007, Combinatorial congruences and Stirling numbers, Acta Arith. 126 (2007), no. 4, 387-398, gen>

Sun Z-W.2011b, Super congruences and Euler numbers, Sci. China Math. 54 (2011), no. 12, 2509-2535,  , nat>

Sun Z-W.2011c, On congruences related to central binomial coefficients, J. Number Theory, 131 (2011), no. 11, 2219-2238, jou>

Sun Z-W.2012a, On sums of Apéry polynomials and related congruences, J. Number Theory, Vol. 132, Issue 11, Nov. 2012, 2673-2699, jou>

Sun Z-W.2014, Congruences involving generalized central trinomial coefficients, Sci. China Math. 2014, Vol. 57, Issue 7, 1375-1400, nat>

Sun Z-W.Tauraso2007, Congruences for sums of binomial coefficients, J. Number Theory, Vol. 126, Issue 2, Oct 2007, 287-296, jou>

Sun Z-W.Tauraso2011, On some new congruences for binomial coefficients, Int. J. Number Theory, 07 (2011), No. 3, 645–662, gen>

Tauraso2016, Some congruences for central binomial sums involving Fibonacci and Lucas numbers, J. Integer Seq. Vol. 19 (2016), Article 16.5.4, jis>

Young1994, p-adic congruences for generalized Fibonacci sequences, Fibonacci Quart. 1994 (32,1):  2-10, fibqy>

Young2003b, Congruences for degenerate number sequences, Discrete Math. Vol. 270, Issues 1–3, 28 Aug 2003, 279-289, gen>

Zhao L-L.PanSun Z-W.2010, Some congruences for the second-order Catalan numbers, Proc. Amer. Math. Soc. 138 (2010) , no. 1, 37-46, nat>

Zhou2003, Applications of matrix theory to congruence properties of kth-order F-L sequences, Fibonacci Quart. 2003 (41,1):  48-58, fibqy>,

connection coefficients

Andrews1979, Connection coefficient problems and partitions, Proceedings of Symposium in Pure Math. Vol. 34, 1979, gen>

AokiOhno2005, Sum relations for multiple zeta values and connection formulas for the Gauss hypergeometric functions, Publ. RIMS, Kyoto Univ. 41 (2005), 329-337, nat>

Barry2013d, On the connection coefficients of the Chebyshev-Boubaker polynomials, The Scientific World J. Vol. 2013 (2013), Article ID 657806, 10 p, gen>

ChaggaraKoepf2011, On linearization and connection coefficients for generalized Hermite polyn., J. Comp. Appl. Math. Vol. 236, Issue 1, Aug 2011, 65-73, jou>

Szwarc1992, Connection coefficients of orthogonal polynomials, Canad. Math. Bull. Vol. 35 (4), 1992, 548-556, nat>

continued fractions

Barry2009b, Continued fractions and transformations of integer sequences, J. Integer Seq. Vol. 12 (2009), Article 09.7.6, jis>

Barry2013g, Comparing two matrices of generalized moments defined by continued fraction expansions, arXiv (27 Nov 2013), aXv>

BenjaminSuQuinn2000, Counting on continued fractions, Mathematics Magazine, Vol. 73, No. 2, 98-104, Apr 2000, gen>

Brezinski2010, The Italian contribution to the foundation and development of continued fractions, Rend. Semin. Mat. Univ. Politec. Torino Vol. 68, 1 (2010), 1-16, nat>

BultheelGonzalez-VeraHendriksenNjadstad2000, Orthogonal rational functions and continued fractions, Nato Sci. Ser. II Math. Phys. Chem. Vol. 30, 2001, 87-109,  gen>

Denis1990, On generalization of Euler's continued fractions, Indian J. Pure Appi. Math. 1990, nat>

Denis1991, On generalization of certain continued fractions, Indian J. Pure Appi. Math. 1991, nat>

Dumont1995, Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers, Adv. Appl. Math. Vol. 16, Issue 1, 1995, 275-296, gen>

ElizaldeMansour2006, Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials, arXiv (6 Oct 2006), gen>

Flajolet1980, Combinatorial aspects of continued fractions, Discrete Math. 32 (1980) 125-161, gen>

Frame1949, Continued Fractions and Matrices, Amer. Math. Monthly, Vol. 56, No. 2 (Feb., 1949), 98-103, nat>

Hennessy2011, A study of Riordan arrays with applications to continued fractions, orthogonal polynomials and lattice paths, Thesis-Waterford Institute of Technology (Oct 2011), gen>

LenstraShallit1992, Continued fractions and linear recurrences, Math. Comp. 61, No. 203, Jul 1993, 351-354, gen>

LongJordan1970, A limted arithmetic on simple contined fractions - II, Fibonacci Quart. 1970 (8,2): 135-157, fibqy>

Mansour2002b, Continued fractions and generalized patterns, European J. Combin. Vol. 23, Issue 3, Apr 2002, 329-344, gen>

Mendčs-France vanderPoortenShallit1998, On lacunary formal power series and their continued fraction expansion, To Andrzej Schinzel on his 60th birthday, gen>

Mills1975, Continued Fractions and Linear Recurrences, Math. Comp. Vol. 29, No 129, Jan 1975, 173-180, gen>

Scott1952, The reciprocal of a continued fraction, Proc. Amer. Math. Soc. Vol. 3, No. 5 (Oct 1952), 722-726, nat>

Shallit1982, Explicit descriptions of some continued fractions, Fibonacci Quart. 1982 (20,1): 77-80, fibqy>

ShannonHoradam1988, Generalized Fibonacci continued fractions, Fibonacci Quart. 1988 (26,3): 219-223, fibqy>

van der Poorten1998, Formal power series and their continued fraction expansion, Lect. Notes in Comp. Sci. Vol. 1423, 1998, 358-371-Algorithmic Number Theory, gen>

van der Poorten2005, Elliptic curves and continued fractions, J. Integer Seq. Vol. 8 (2005), Article 05.2.5, jis>

Zeng J.1995, The q-Stirling numbers, continued fractions and the q-Charlier and q-Laguerre polynomials, J. Comp. Appl. Math. Vol. 57, Issue 3, Feb 1995, 413-424, jou>

convolution

Agoh2014, Convolution identities for Bernoulli and Genocchi polynomials, Electron. J. Combin. 21 (1) (2014), gen>

AgohDilcher2007, Convolution identities and lacunary recurrences for Bernoulli numbers, J. Number Theory 124, Issue 1, May 2007, 105-122, jou>

AgohDilcher2008, Generalized convolution identities for Stirling numbers of the second kind, Integers 8 (2008), gen>

AlexanderZagier1991, The entropy of a certain infinitely convovolved Bernoulli measure, J. London Math. Soc. Vol. s2-44, Issue 1 (Aug 1991), 121-134,  nat>

BenderDaalhuisGaoRichmondWormald2010, Asymptotics of some convolutional recurrences, Electron. J. Combin. 17 (2010), gen>

BergumHoggatt, Jr.1976, Numerator polynomial coefficient array for the convolved Fibonacci sequence, Fibonacci Quart. 1976 (14,1):  43-47, fibqy>

BirmajerGilWeiner2015, Linear recurrence sequences and their convolutions via Bell polynomials, J. Integer Seq. Vol. 18 (2015), Article 15.1.2, jis>

Chu2012a, Reciprocal formulae for convolutions of Bernoulli and Euler polynomials, Rend. Mat. Appl. (7), Serie VII Vol. 32, Roma (2012), 17-74, nat>

ChuZhou2010, Convolutions of Bernoulli and Euler polynomials, Sarajevo J. Math. Vol.6 (18) (2010), 147-163, nat>

Di NardoPetrulloSenato2010, Cumulants and convolutions via Abel polynomials, European J. Combin. Vol. 31, Issue 7, Oct 2010, 1792-1804, gen>

Duarte, de Oliveira2013, Note on the convolution of binomial coefficients, J. Integer Seq. Vol. 16 (2013), Article 13.7.6, jis>

FengZhang Z.2003, Computational formulas for convoluted generalized Fibonacci and Lucas numbers, Fibonacci Quart. 2003 (vol.41,2): 144-151, fibqy>

Flensted-JensenKoornwinder1973, The convolution structure for Jacobi function expansions, Arkiv för Matematik 1973, Vol. 11, Issue 1-2, 245-262, nat>

Glaeske2000, Convolution structure of (generalized) Hermite transforms, Banach Center Publ. Vol. 53, nat>

Gould2002, Generalized Bernoulli and Euler polyn. convolution identities, xxxx, xxxx>

Hoggatt, Jr.1970, Convolution triangles for generalized Fibonacci numbers, Fibonacci Quart. 1970 (8,2): 158-171, fibqy>

Hoggatt, Jr.Bergum1975, Generalized convolution arrays, Fibonacci Quart. 1975 (13,3):  193-197, fibqy>

Hoggatt, Jr.Bicknell1972, Convolution triangles, Fibonacci Quart. 1972 (10,6): 599-608, fibqy>

Hoggatt, Jr.Bicknell1976a, Pascal, Catalan, and general sequence convolution arrays in a matrix, Fibonacci Quart. 1976 (14,2): 135-143, fibqy>

Hoggatt, Jr.Bicknell-Johnson1978b, Convolution arrays for Jacobsthal and Fibonacci polynomials, Fibonacci Quart. 1978 (16,5): 385-402, fibqy>

Kim2014, Bernoulli polynomials and convolution sums, British J. of Math. and Computer Sci. 4 (3): 363-374, 2014, nat>

Knuth1992(Jul arxiv)1992, Convolution polynomials, arXix (1 Jul 1992), aXv>

Liu2002, Formulas for convolution Fibonacci numbers and polynomials, Fibonacci Quart. 2002 (40,4): 352-357, fibqy>

Mikic2016, A proof of a famous identity concerning the convolution of the central binomial coefficients, J. Integer Seq. Vol. 19 (2016), Article 16.6.6, jis>

Moree2004, Convoluted convolved Fibonacci numbers, J. Integer Seq. Vol. 7 (2004), Article 04.2.2, jis>

NguyenCheong2014, New convolution identities for hypergeometric Bernoulli polynomials, J. Number Theory Vol. 137, April 2014, 201-221, jou>

Pan2013, Convolution properties of the generalized Stirling numbers and the Jacobi-Stirling numbers of the first kind, J. Integer Seq. Vol. 16 (2013), Article 13.9.2, jis>

Sofo2000a, A convoluted Fibonacci sequence - Part I, RGMIA Research Report Collection (Vol.3,2): 1-7, gen>

Sofo2000b, A convoluted Fibonacci sequence - Part II, Austral. Math. Soc. Gaz. 27; 107-114, nat>

Velasco2010, Convolution and Sulanke Numbers, J. Integer Seq. Vol. 13 (2010), Article 10.1.8, jis>

Yang Y.2004, Generating functions of convolution matrices, Proc. 10th Int. Research Conf. on Fibonacci numbers and their applications, Vol. 9, gen>

cumulants

Di NardoPetrulloSenato2010, Cumulants and convolutions via Abel polynomials, European J. Combin. Vol. 31, Issue 7, Oct 2010, 1792-1804, gen>

Di NardoSenato2006, An umbral setting for cumulants and factorial moments, European J. Combin. Vol. 27, Issue 3, Apr 2006, 394-413, gen>

Lehner2003, Cumulants, lattice paths, and orthogonal polynomials, Discrete Math. Vol. 270, Issues 1–3, Aug 2003, 177-191, gen>

Petrullo2009, Cumulants and classical umbral calculus, 62nd Sém. Lothar. Combin. Heilsbronn (Germany), Feb 22-25, 2009, gen>

RotaShen2000, On the combinatorics of cumulants, J. Combin. Theory Ser. A, Vol. 91, Issues 1–2, Jul 2000, 283-304, jou>

Daehee

JangKwonRimSeo2014, A note on q-analogue of lambda-Daehee polynomials, Adv. Studies Theor. Phys., Vol. 8, 2014, no. 13, 589-597, gen>

Kim D.S.Kim T.2014b, Some properties of higher-order Daehee polynomials of the second order arising from umbral calculus, J. Inequal. Appl. 2014, 2014: 195, jou>

Kim D.S.Kim T.KomatsuSeo2014, Barnes-type Daehee polynomials, arXiv (14 Jan 2014), aXv>

KimKim2013f, Daehee numbers and polynomials, arXiv (9 Sep 2013), aXv>

KimKim2013h, Higher-order Daehee numbers and polynomials, arXiv (17 Oct 2013), aXv>

ParkRimKwon2013, The hyper-geometric Daehee umbers and polynomials, Turkish J. of Analysis and Number Theory 2013, Vol. 1, No. 1, 59-62, nat>

degenerate numbers, degenerate polynomials

Adelberg1995, A finite difference approach to degenerate Bernoulli and Stirling polynomials, Discrete Math. 140 (1995), 1-21, gen>

DangiTiwariParihar2013, Generalized degenerated Bernoulli numbers and polynomials, J. Int. Acad. Phys. Sci. Vol. 17, No.3 (2013), 245-254, jou>

Dilcher2008, Determinant expressions for q-harmonic congruences and degenerate Bernoulli numbers, Electron. J. Combin. 15 (2008), gen>

GabouryTremblay2014, A further investigation of gener. funct. related to pairs of inverse funct. with appl. to gener. degenerate Bernoulli polyn., Bull. Korean Math. Soc. 51 (2014), No. 3, 831-845, nat>

Howard1979, Bell polynomials and degenerate Stirling numbers, Rend. Semin. Mat. Univ. Padova, tome 61 (1979), 203-219, nat>

KimKimDolgy2015, A note on degenerate Bernoulli numbers and polynomials associated with p -adic invariant integral on Zp, Appl. Math. Comput. Vol. 259, May 2015, 198-204, gen>

RamprasadMadhuParihar2013, Degenerated Bernoulli numbers and polynomials, Int. J. of Physics and Mathemat.Sci. 2013 Vol. 3 (4) Oct-Dec, 23-29, gen>

Young2008, Degenerate Bernoulli polynomials, generalized factorial sums, and their applications, J. Number Theory Vol. 128, Issue 4, Apr 2008, 738-758, jou>

Delannoy

BanderierSchwer2005, Why Delannoy numbers?, J. Statist. Plann. Inference Vol. 135, Issue 1, Nov 2005, 40–54, jou>

Dziemianczuk2013, Generalizing Delannoy numbers via counting weighted lattice paths, Integers 13 (2013), 1-33, gen>

Hetyei2008, Delannoy numbers and a combinatorial proof of the orthogonality of the Jacobi polynomials with natural number parameters, 23rd Clemson mini-Conference on Discrete Math. and Algorithms, Clemson, SC, Oct 2, 2008, gen>

Hetyei2009, Shifted Jacobi polynomials and Delannoy numbers, arXiv (24 Dec 2009), aXv>

Sun Z-W.2011a, On Delannoy numbers and Schröder numbers, J. Number Theory, Vol. 131, Issue 12, Dec 2011, 2387-239Z, jou>

Yang S-l.ZhengYuanHe2013, Schröder matrix as inverse of Delannoy matrix, Linear Algebra Appl. Vol. 439, Issue 11, Dec 2013, 3605-3614, gen>

Denert statistic

HanZeng1999a, q-polynômes de Gandhi et statistique de Denert, Discrete Math. Vol. 205, Issues 1–3, 28 July 1999, 119-143, gen>

dérangements, dérangements q-analogues

BriggsRemmel2009, A p, q-analogue of the generalized derangement numbers, Ann. Comb. 13 (2009) 1-25, gen>

ChenDengYang2008, Riordan paths and derangements, Discrete Math. Vol. 308, Issue 11, Jun 2008, 2222-2227, gen>

ClarkeHanZen1997, A combinatorial interpretation of the Seidel generation of q-derangement numbers, Annals Comb. 1997, Vol. 1, Issue 1, 313-327, gen>

DelfertEinzigerRawlings2003, The derangement problem relative to the Mahonian process, Int. J. Math. Math. Sci. Vol. 2003 (2003), Issue 24, 1497-1508, gen>

DumontRandrianarivony1994, Dérangements et nombres de Genocchi, Discrete Math. Vol. 132, Issues 1–3, Sep 1994, 37-49, gen>

FoataZeilberger1988, Laguerre polynomials, weighted dérangements, and positivity, Siam J. Disc. Math. Vol. 1, No. 4, Nov1988, gen>

Hassani2003, Derangements and applications, J. Integer Seq. Vol. 6 (2003), Article 03.1.2, jis>

KimZeng2001, A new decomposition of derangements, J. Combin. Theory Ser. A, Vol. 96, Issue 1, Oct 2001, 192-198, jou>

Sun P.2005, A note on the number of derangements, Appl. Math. E-Notes, 5 (2005), 176-178, gen>

Diophantine equations

BugeaudMignotteSiksek2006a, Classical and modular approaches to exponential diophantine equations I. Fibonacci and Lucas perfect powers, Ann. of Math. (2), 163 (2006), 969-1018,  nat>

BugeaudMignotteSiksek2006b, Classical and modular approaches to exponential diophantine equations II. The Lebesgue–Nagell equation, Compos. Math. 142 (2006) 31–62, gen>

CorvajaZannier1998, Diophantine equations with power sums and universal Hilbert sets, Indag. Mathem., N.S., 9 (3), Sep. 1998, 317-332, gen>

Halter-Koch2011, Diophantine equations of Pellian type, J. Number Theory Vol. 131, Issue 9, Sep 2011, 1597-1615, jou>

Prévost2000, Diophantine approximations using Padé approximations, J. Comp. Appl. Math. 122 (2000) 231-250, jou>

ShoreyStewart1987, Pure powers in recurrent sequences and some related Diophantine equations, J. Number Theory Vol, 27, Issue 3, Nov 1987, 324-352, jou>

Tengely2005, Effective methods for Diophantine equations, Doctor aan de Universiteit Leiden, gen>

Zannier2005, Diophantine equations with linear recurrences An overview of some recent progress, J. Théor. Nombres Bordeaux 17 (2005), 423-435, nat>

Dobinski

Kwasniewski2005, On psi-umbral extensions of Stirling numbers and Dobinski-like formulas, arXiv (20 Oct 2005), aXv>

Dumont-Foata

Carlitz1980a, Explicit formulas fot the Dumont-Foata polynomial, Discrete Math. Vol. 30, Issue 3, 1980, 211-225, gen>

Ehrhart

Chapoton2013, q-analogues of Ehrhart polynomials, arXiv (23 Fev 2013), aXv>

ChenLiSam2010, Generalized Ehrhart polynomials, Trans. Amer. Math. Soc. 364 (2012), 551-569, nat>

elliptic (see also Jacobi)

Berndt2000, Flowers which we cannot yet see growing in Ramanujan’s garden of hypergeometric series, elliptic functions, and q ’s, Nato Sci. Ser. II Math. Phys. Chem. Vol. 30, 2001, 61-85, gen>

BianePitmanYor2001, Probability laws related to the Jacobi theta and Riemann z-functions, and Brownian motion excursions, Bull. Amer. Math. Soc. (N.S.) Vol. 38, no. 4, 435-465, nat>

Dumont1981, Une approche combinatoire des fonctions elliptiques de Jacobi, Adv. Math. Vol. 41, Issue 1, Jul 1981, 1-39, gen>

Flensted-JensenKoornwinder1973, The convolution structure for Jacobi function expansions, Arkiv för Matematik 1973, Vol. 11, Issue 1-2, 245-262, nat>

Koelink1995, Identities for q-ultraspherical polynomials and Jacobi functions, Proc. Amer. Math. Soc. 123 (1995), 2479-2487, nat>

Silverman2006, An introduction to the theory of elliptic curves, Summer School on Comput. Number Theory, Univ. of Wyoming (Jul 2006), gen>

Viennot1980, Une interprétation combinatoire des coefficients des développements en série entičre des fonctions elliptiques de Jacobi, J. Combin. Theory Ser. A, Vol. 29, Issue 2, Sep 1980, 121-133, jou>

embedding distributions, structures

Barry2014c, Embedding structures associated with Riordan arrays and moment matrices, Int. J. Comb. Vol. 2014 (2014), Article ID 301394, 7 p, gen>

ChenMansourZou2012, Embedding distributions and Chebyshev polynomials, Graphs and Combinatorics Vol. 28, Issue 5 , 597-614, gen>

entropy

Abramov R.V.2010, The multidimensional maximum entropy moment problem: A review on numerical methods, Commun. math. sci. 8(2010), June 2010, gen>

AlexanderZagier1991, The entropy of a certain infinitely convolved Bernoulli measure, J. London Math. Soc. Vol. s2-44, Issue 1 (Aug 1991), 121-134, jou>

CarliFerrantePavonPicci2013, An efficient algorithm for maximum entropy extension of block-circulant covariance matrices, Linear Algebra Appl. Vol. 439, Issue 8, 15 Oct 2013, 2309–2329 arXiv (8 Feb 2013), aXv>

Erkus-Srivastava

SrivastavaNisarKhan2014, Some umbral calculus presentations of the Chan-Chyan-Srivastava polyn. and the Erkus-Srivastava polyn., Proyecciones, Vol. 33, No 1, 77-90, Mar 2014, gen>

Euler

1, 2006, 102-107, gen>

Arreghi2001b, Bernoulli and Euler numbers, Motzkin paths and numerical triangles, Pre-publicaciones del Seminario Matemático "García de Galdeano", Nş. 34, 2001, gen>

BayadHamahata2012, Identities involving two kinds of q-Euler polynomials and numbers, J. Integer Seq. Vol. 15 (2012), Article 12.4.6, jis>

BorweinCalkinManna2009, Euler-Boole summation revisited, Amer. Math. Monthly, Vol. 116, No. 5 (May, 2009), 387-412, nat>

Boyadzhiev2009, Harmonic number identities via Euler’s transform, J. Integer Seq. Vol. 12 (2009), Article 09.6.1, jis>

Byrd1975b, Relations between Euler and Lucas numbers, Fibonacci Quart. 1975 (13,2): 111-114, fibqy>

Chen2001, Algorithms for Bernoulli numbers and Euler numbers, J. Integer Seq. Vol. 4 (2001), Article 01.1.6, jis>

Chen2004, Congruences for Euler numbers, Fibonacci Quart. 2004 (42,2): 128-140, fibqy>

Chen2006, Evaluations of some variant Euler sums, J. Integer Seq. Vol. 9 (2006), Article 06.2.3, jis>

Dumont1995, Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers, Adv. Appl. Math. Vol. 16, Issue 1, 1995, 275-296, gen>

Ernst2006, q-Bernoulli and q-Euler polynomials, an umbral approach, Int. J. Differ. Equ. Vol. 1, No. 1, (2006), 31–80, gen>

Gould2002, Generalized Bernoulli and Euler polynomial convolution identities, xxxx, xxxx>

HuberYee2010, Combinatorics of generalized q-Euler numbers, J. Combin. Theory Ser. A, Vol. 117, Issue 4, May 2010, 361-388, jou>

Kim D.S.2011, Identities of symmetry for q-Euler polynomials, Open J. Discrete Math. 2011, 1, 22-31, gen>

Kim T.2010, New approach to q-Euler polynomials of higher order, Russ. J. Math. Phys. Jun 2010, Vol. 17, Issue 2, 218-225, nat>

Kim2007a, The modified q-Euler numbers and polynomials, arXiv (18 Fev 2007), aXv>

Kim2009a, q-Euler numbers and polynonials associated with multiple q-zeta functions, arXiv (24 Dec 2009), aXv>

Kim2009b, Barnes type multiple q-zeta functions and q-Euler polynomials, arXiv (28 Dec 2009), aXv>

KimHwangKim2009, Sums of products of q-Euler polynomials and numbers, J. Inequal. Appl. Vol. 2009, Article ID 381324, 8 p, jou>

KimKim2012d, Arithmetic identities involving Bernoulli and Euler numbers, Int. J. Math. Math. Sci. Vol. 2012 (2012), Article ID 689797, 10 p, gen>

KimKimDolgy2012, Some identities on Laguerre polynomials in connection with Bernoulli and Euler numbers, Discrete Dyn. Nat. Soc. Vol. 2012, Article ID 619197, 10 p, gen>

KimKimDolgyRim2013, Some identities of higher-order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus, J. Inequal. Appl. 2013, 2013: 211, jou>

KimKimLeeDolgyRim2011, Some new identities on the Bernoulli and Euler numbers, Discrete Dyn. Nat. Soc. Vol. 2011, Article ID 856132, 11 p, gen>

KimKurtKurt2013, Some identities on the generalized q-Bernoulli, q-Euler, and q-Genocchi polynomials, Abstr. Appl. Anal. Vol. 2013, Article ID 293532, 6 p., gen>

KimRim2007, New Changhee q-Euler numbers and polynomials associated with p-adic q-integrals, Comput. Math. Appl. Vol. 54, Issue 4, Aug 2007, 484-489, gen>

KimRimSimsekKim2008, On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions, J. Korean Math.  45 (2008), No. 2, 435-453, nat>

LeeKim2012, Derivation of identities involving Bernoulli and Euler numbers, Int. J. Math. and Mathematical Sciences, Vol. 2012 (2012), Article ID 598543, 14 p, gen>

Liu2006, Congruences for higher-order Euler numbers, Proc. Japan Acad. 82, Series A, (2006), No. 3, 30-33, nat>

LucaHuguetNicolae2009, On the Euler function of Fibonacci numbers, J. Integer Seq. Vol. 12 (2009), Article 09.6.6, jis>

LuoQi2003, Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 7 (2003), No. 1, 11-18, gen>

LuoQiDebnath2003, Generalizations of Euler numbers and polynomials, Int. J. of Math. and Mathematical Sciences, Vol. 2003 (2003), Issue 61, 3893-3901, gen>

Mahmudov2013, On a class of q-Bernoulli and q-Euler polynomials, Adv. Difference Equ. 2013, 2013: 108, gen>

MahmudovKeleshteri2013, On a class of generalized q-Bernoulli and q-Euler polynomials, Adv. Difference Equ. 2013, 2013: 115, gen>

MahmudovMomemzadeh2014, On a class of q-Bernoulli, q-Euler and q-Genocchi polynomials, arXiv (18 Jan 2014), aXv>

MasonHudson2004, A generalization of Euler's formula and its connection to Fibonacci numbers, Proc. 10th int. Conf. on Fibonacci numbers and their Applic. 2004, Vol. 9, 177-185, gen>

NalliZhang2010, On generalized Lucas polynomials and Euler numbers, Miskolc Mathematical Notes Vol. 11 (2010), No. 2, 163-167,  nat>

PanSun Z-W.2006b, On q-Euler numbers, q-Salié numbers and q-Carlitz numbers, Acta Arith. 124 (2006), no. 1, 41-57, gen>

RyooKimJang2007, Some relationships between the analogs of Euler numbers and polynomials, J. Inequal. Appl. Vol. 2007, Article ID 86052, 22 p, jou>

Shparlinski2006, On the sum of Iterations of the Euler function, J. Integer Seq. Vol. 9 (2006), Article 06.1.6, jis>

Sofo2012b, Euler-related sums, Mathematical Sciences 2012, 6:10, gen>

Srivastava2011, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inf. Sci. 5 (3) (2011), 390-444, gen>

Sun Z-W.2011b, Super congruences and Euler numbers, Sci. China Math. 54 (2011), no. 12, 2509-2535, nat>

Sun Z-W.Pan2006, Identities concerning Bernoulli and Euler polynomials, Acta Arith. 125 (2006), no. 1, 21-39, gen>

Szablowski2014, A few remarks on Euler and Bernoulli polyn. and their connections with binom. coef. and modified Pascal matrices, Math. Ćterna, Vol. 4, 2014, no. 1, 83-88, gen>

Tempesta2006, On a generalization of Bernoulli and Euler polynomials, arXiv (27 Jan 2006), aXv>

Tempesta2008, On Appell sequences of polynomials of Bernoulli and Euler type, J. Math. Anal. Appl. Vol. 341, Issue 2, May 2008, 1295-1310, jou>

Toscano1978, Some results for generalized Bernoulli, Euler, Stirling numbers, Fibonacci Quart. 1978 (16,2): 103-111, fibqy>

Velasco2012, A note on Fibonacci and Lucas and Bernoulli and Euler polynomials, J. Integer Seq. Vol. 15 (2012), Article 12.2.7, jis>

Vella2008, Explicit formulas for Bernoulli and Euler numbers, Integers 8 (2008), gen>

Wang H.Liu2013a, Some properties of a sequence similar to generalized Euler numbers, Discrete Math. Vol. 2013, Article ID 810245, 5 p, gen>

Yi2006, Some identities involving Bernoulli numbers and Euler numbers, Scientia Magna Vol. 2, No. 1, 2006, 102-107, gen>

Euler-Barnes

JangKim2005, q-analogue of Euler-Barnes' numbers and polynomials, Bull. Korean Math. Soc. 42 (2005), No. 3, 491-499, nat>

Kim2006b, q-analogue of Euler- Barnes multiple zeta functions, arXiv (6 Mar 2006), aXv>

Euler-Bernoulli

Liu2001, Identities and congruences involving higher-order Euler-Bernoulli numbers and polynomials, Fibonacci Quart. 2001 (39,3): 279-284, fibqy

Euler-Frobenius

ChoiKimKimKim2012, A note on some identities of Frobenius-Euler numbers and polynomials, Int. J. Math. and Mathematical Sciences, Vol. 2012 (2012), Article ID 861797, 9 p, gen>

GawronskiNeuschel2013, Euler–Frobenius numbers, Integral Transforms Spec. Funct. Vol. 24, Issue 10, 2013, 817-830,  gen>

Janson2013, Euler-Frobenius numbers and rounding, arXiv (15 May 2013), aXv>

KimKim2012e, Some identities of Frobenius-Euler polynomials arising from umbral calculus, Adv. Difference Equ. 2012, 2012: 196, gen>

KimKimRimDolgy2013b, Some identities of Frobenius-type Eulerian polynomials arising from umbral calculus, Int. J. Math. Anal. (Ruse), Vol. 7, 2013, no. 53, 2637-2644, gen>

KimMansour2014, Umbral calculus associated with Frobenius-type Eulerian polynomials, Russ. J. Math. Phys. Jun 2014, Vol. 21, Issue 4, 484-493, nat>

Euler-Seidel

BarryHennessy2010a, The Euler-Seidel matrix, Hankel matrices and moment sequences, J. Integer Seq. Vol. 13 (2010), Article 10.8.2, jis>

MezňDil2009, Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence, Cent. Eur. J. Math. Jun 2009, Vol. 7, Issue 2, 310-321, gen>

Tutas2014, Euler-Seidel matrices over Fp, Turkish J. of Math. (2014) 38: 16-24, nat>

Eulerian

AraciAcikgozSen2014b, New generalization of Eulerian polynomials and their applications, J. Ana. Num. Theor. 2, No. 2, 59-63 (2014),  jou>

Barry2011d, Eulerian polynomials as moments, via exponential Riordan arrays, J. Integer Seq. Vol. 14 (2011), Article 11.9.5, jis>

Barry2013e, General Eulerian polynomials as moments using exponential Riordan arrays, J. Integer Seq. Vol. 16 (2013), Article 13.9.6, jis>

Carlitz1954, q-Bernoulli and Eulerian numbers, Trans. Amer. Math. Soc. Vol. 76, No. 2 (Mar 1954), nat>

Carlitz1959b, Eulerian numbers and polynomials, Math. Magazine Vol. 32, No. 5 (May - Jun 1959), 247-260, gen>

Carlitz1960b, Eulerian numbers and polynomials of higher order, Duke Math. J. Vol. 27, No. 3 (1960), 401-423, gen>

Carlitz1963a, The product of two Eulerian polynomials, Math. Magazine, Vol. 36, No. 1 (Jan 1963), 37-41, gen>

Carlitz1973, Eulerian numbers and operators, Lecture Notes in Math. 1971, 65-70 -The Theory of Arith. Funct., gen>

CarlitzHoggath, Jr.1978, Generalized Eulerian numbers and polynomials, Fibonacci Quart. 1978 (16,2): 138-146, fibqy>

CarlitzScoville1975, Eulerian numbers and operators, Fibonacci Quart. 1975 (13,1): 71-83, fibqy>

ChangHa2002, Eulerian polynomials and related explicit formulas, Fibonacci Quart. 2002 (40,5): 399-404, fibqy>

ChungGrahamKnuth2010, A symmetrical Eulerian identity, J. Comb. Vol. 17, No. 1, 29-38, 2010, jou>

de OliveraBergmannOnusic2013, A limit to represent Bernoulli numbers using Eulerian numbers, Int. J. Pure Appl. Math. Vol. 83 No. 4, 2013, 589-599,  gen>

EhrenborgReaddy2006, Characterization of Eulerian binomial and Sheffer posets, Formal Power Series and Algebraic Combinatorics-San Diego, California 2006, gen>

ErmanSmithVarilly-Alvarado2011, Laurent polynomials and Eulerian numbers, J. Combin. Theory Ser. A, Vol. 118, Issue 2, Feb 2011, 396-402, gen>

FoataZeilberger1991, Multibasic Eulerian polynomials, Trans. Amer. Math. Soc. Vol. 328, No. 2, (Nov 1991), 843-862, nat>

KimKimKimDolgy2012, A note on Eulerian polynomials, Abstr. Appl. Anal. Vol. 2012 (2012), Article ID 269640, 10 p,  gen>

KimKimRimDolgy2013b, Some identities of Frobenius-type Eulerian polynomials arising from umbral calculus, Int. J. Math. Anal. (Ruse), Vol. 7, 2013, no. 53, 2637-2644, gen>

KimMansour2014, Umbral calculus associated with Frobenius-type Eulerian polynomials, Russ. J. Math. Phys. Jun 2014, Vol. 21, Issue 4, 484-493, nat>

Koutras1994, Eulerian numbers associated with sequences of polynomials, Fibonacci Quart. 1994 (vol.32,1): 44-57, fibqy>

NymannSaenz1999, Eulerian numbers: inversion formulas and congruences modulo a prime, Fibonacci Quart. 1999 (37,2): 154-161, fibqy>

ShareshianWachs2007, q-Eulerian polynomials: excedence number and major index, Electr. Research Announcements of the Amer. Math. Soc. Vol. 13, 33-45 (Apr 12, 2007),  nat>

Simsek2013a, Generating function for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications, Fixed Point Theory Appl. 2013, 2013: 87, gen>

Simsek2013b, Identities associated with generalized Stirling type numbers and Eulerian type polyn., Math. Comput. Appl. Vol. 18, No. 3, 251-263, 2013, gen>

Wang X.Hsu2003, A summation formula for power series using Eulerian fractions, Fibonacci Quart. 2003 (vol.41,1): 23-30, fibqy>

XiongHallTsao2014, Combinatorial interpretation of general Eulerian numbers, J. Discrete Math. Vol. 2014 (2014), Article ID 870596, 6 p, jou>

XiongTsaoHall2013, General Eulerian numbers and Eulerian polynomials, J. of Math. Vol. 2013, Article ID 629132, 9 p, jou>

ZengZhang1994, A q-analog of Newton’s series, Stirling functions and Eulerian functions, Results Math. May 1994, Vol. 25, Issue 3-4, 370-391, gen>

Faber

Airault2008, Remarks on Faber polynomials, Int. Math. Forum 3, 2008, no. 9, 449-456, gen>

AiraultBouali2006, Differential calculus on the Faber polynomials, Bull. Sci. Math. Vol. 130, Issue 3, Apr–May 2006, 179-222, nat>

Jabotinsky1953, Representation of functions by matrices. Application to Faber polynomials, Proc. of the Amer. Math. Society Vol. 4, No. 4 (Aug., 1953), 546-553, nat>

Kuijlaars1995, Chebyshev-type quadrature and zeros of Faber polynomials, J. Comput. Appl. Math. Vol. 62, Issue 2, Sep 1995, 155-179, jou>

Schur1945, On Faber polynomials, Amer. J. Math. Vol. 67, No. 1 (Jan., 1945), 33-41, nat>

Todorov1981, Explicit formulas for the coefficients of Faber polynomials with respect to univalent functions of the class S, Proc. Amer. Math. Soc. Vol. 82, Number 3, Jul 1981, nat>

Todorov1991, On the Faber polynomials of the univalent functions of class S, J. Math. Anal. Appl. Vol. 162, Issue 1, Nov 1991, 268-276, jou>

Zayed1990, Jacobi polynomials as generalized Faber polynomials, Trans. Amer. Math. Soc. Vol. 321, No. I, Sep 1990, nat>

factorial generalizations

Pan2012, Matrix decomposition of the unified generalized Stirling numbers and inversion of the generalized factorial matrices, J. Integer Seq. Vol. 15 (2012), Article 12.6.6, jis>

Schmidt2010, Generalized j-factorial functions, polynomials, and applications, J. Integer Seq. Vol. 13 (2010), Article 10.6.7, jis>

SongCheonJunBeasley2010, A q-analogue of the generalized factorial numbers, J. Korean Math. Soc. 47 (2010), No. 3, 645-657, nat>

Young2008, Degenerate Bernoulli polynomials, generalized factorial sums, and their applications, J. Number Theory Vol. 128, Issue 4, Apr 2008, 738-758, jou>

Fibonacci

AharonovBeardonDriver2005, Fibonacci, Chebyshev, and orthogonal polynomials, Amer. Math. Monthly Vol. 112, No. 7 (2005), 612-630, nat>

AkyuzHalici2013, On some combinatorial identities involving the terms of generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat. Vol. 42 (4) (2013), 431-435,  gen>

Alfred1963, Exploring Fibonacci numbers, Fibonacci Quart. 1963 (1,1): 57-63, fibqy>

AmdeberhanChenMollSagan2014, Generalized Fibonacci polynomials and Fibonomial coefficients, Ann. Comb. (2014) Vol.18, Issue 4: 541-562, gen>

AndradePethe1992, On the rth-order nonhomogeneous recurrence relation and some generalized Fibonacci sequences, Fibonacci Quart. 1992 (30,3): 256-262, fibqy>

AndradeSantosdaSilvaSilva2013, Polyn. generalizations and combin. interpretations for seq. including the Fibonacci and Pell numbers, Open J. Discrete Math. 2013, 3, 25-32, gen>

Andrews1969, Some formulae for the Fibonacci sequence with generalizations, Fibonacci Quart. 1969 (7,2): 113-130, fibqy>

Antoniadis1985, Fibonacci and Lucas numbers of the form 3z^2 + 1, Fibonacci Quart. 1985 (23,4): 300-307, fibqy>

ArdalGundersonJungicLandmanWilliamson2008-09, Ramsey results involving the Fibonacci numbers, Fibonacci Quart. 2008-09 (46-47,1): 10-17, fibqy>

ArkinHoggatt, Jr.1970, An extension of Fibonacci numbers -- II, Fibonacci Quart. 1970 (8,2): 199-216, fibqy>

Asveld1987, A family of Fibonacci like sequences, Fibonacci Quart. 1987 (25,1): 81-83, fibqy>

AtanassovAtanassovaSasselov1985, A new perspective to the generalization of the Fibonacci sequence, Fibonacci Quart. 1985 (23,1): 21-28, fibqy>

AtanassovHleBarskaMihov1992, Recurrent formulas of the generalized Fibonacci and Tribonacci sequences, Fibonacci Quart. 1992 (30,1): 77-79, fibqy>

BadshahTeethDar2012, Generalized Fibonacci-like sequence and its properties, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 21-24, 1155-1164, gen>

BelbachirBelkhir2014, Combinatorial expressions involving Fibonacci, hyperfibonacci, and incomplete Fibonacci numbers, J. Integer Seq. Vol. 17 (2014),Article 14.4.3, aXv>

BelbachirBencherif2007, Sums of products of generalized Fibonacci and Lucas numbers, arXiv (17 Aug 2007), aXv>

BelbachirBencherif2008, On some properties of bivariate Fibonacci and Lucas polynomials, J. Integer Seq. Vol. 11 (2008), Article 08.2.6, jis>

BelbachirBenmezai2012, Expansion of Fibonacci and Lucas polynomials: An answer to Prodinger’s question, J. Integer Seq. Vol. 15 (2012), Article 12.7.6, jis>

BenjaminCameronQuinn2007, Fibonacci determinants - a combinatorial approach, Fibonacci Quart. 45(1): 39-55. Claremont Colleges - HMC Faculty Scholarship, fibqy>

BenjaminHeberle2014, Counting on r-Fibonacci numbers, Fibonacci Quart. 52 (2014), no. 2, 121-128, fibqy>

BenjaminQuinn2005-2006, Revisiting Fibonacci and related sequences, Math. Teacher, Vol. 99, No. 5 (2005-2006), gen>

Berg2011, Fibonacci numbers and orthogonal polynomials, Arab J. Math. Sci. Vol. 17, Issue 2, Jul 2011, 75-88, nat>

BernoussiMottaRachidiSaeki2001, Approximation of infinite generalized Fibonacci sequences and their asymptotic Binet formula, Fibonacci Quart. 2001 (39,2): 168-180, fibqy>

Bernstein1976, A formula for Fibonacci numbers from a new approach to generalized Fibonacci numbers, Fibonacci Quart. 1976 (14,4): 358-367, fibqy>

Bicknell-Johnson2003, Stern's diatomic array applied to Fibonacci representations, Fibonacci Quart. 2003 (41,2): 169-179, fibqy>

Bilcigi2014, New generalizations of Fibonacci and Lucas sequences, Appl. Math. Sci. Vol. 8, 2014, no. 29, 1429-1437, gen>

Bollinger1984, Fibonacci k-sequences, Pascal-T triangles, and k-in-a-row problems, Fibonacci Quarterly 1984 (22,2): 146-151, fibqy>

Bouras2013, A new characterization of Catalan numbers related to Hankel transforms and Fibonacci numbers, J. Integer Seq. Vol. 16 (2013), Article 13.3.3, jis>

Brousseau1969b, Summation of infinite Fibonacci series, Fibonacci Quart. 1969 (7,2): 143-168, fibqy>

Brousseau1972, A note on the number of Fibonacci sequences, Fibonacci Quart. 1972 (10,6): 657-658, fibqy>

Bruckner1970, Fibonacci sequence modulo a prime p ≡ 3 (mod 4), Fibonacci Quart. 1970 (8,2): 217-220, fibqy>

Bunder1978, More Fibonacci functions, Fibonacci Quart. 1978 (16,2): 97-98, fibqy>

Buschman1963, Fibonacci numbers, Chebyshev polynomials, generalizations and difference equations, Fibonacci Quart. 1963 (1,4): 1-7, fibqy>

Byrd1963, Expansion of analytic functions in polynomials associated with Fibonacci numbers, Fibonacci Quart. 1963 (1,1): 16-27, fibqy>

Byrd1975a, New relations between Fibonacci and Bernoulli numbers, Fibonacci Quart. 1975 (13,1): 59-69, fibqy>

CahillD'ErricoSpence2003, Complex factorization of the Fibonacci and Lucas numbers, Fibonacci Quart. 2003 (vol.41,1): 13-19, fibqy>

CaoZhao F-Z.2010, Some properties of hyperFibonacci and hyperLucas numbers, J. Integer Seq. Vol. 13 (2010), Article 10.8.8, jis>

CapocelliCull2003, Rounding the solutions of Fibonacci-like difference equations, Fibonacci Quart. 2003 (41,2): 133-141, fibqy>

Carlitz1968b, Fibonacci representations, Fibonacci Quart. 1968 (6,4): 193-220, fibqy>

Carlitz1970, Fibonacci representations -- II, Fibonacci Quart. 1970 (8,2): 113-134, fibqy>

Carlitz1974a, Fibonacci notes -- 3: q-Fibonacci numbers, Fibonacci Quart. 1974 (12,4): 317-322, fibqy>

Carlitz1975a, Fibonacci notes--4: q-Fibonacci polynomials, Fibonacci Quart. 1975 (13,2):  97-102, fibqy>

Carlitz1978b, Some classes of Fibonacci sums, Fibonacci Quart. 1978 (16,5): 411-425, fibqy>

CarlitzScovilleVaughan1973, Some arithmetic functions related to Fibonacci numbers, Fibonacci Quart. 1973 (11,4): 337-386, fibqy>

Cerda-Morales2013, On generalized Fibonacci and Lucas numbers by matrix methods, Hacet. J. Math. Stat. Vol. 42 (2) (2013), 173-179, gen>

Cereceda2014, Determinantal representations for generalized Fibonacci and tribonacci numbers, Int. J. Contemp. Math. Sci. Vol. 9, 2014, no. 6, 269-285, gen>

Cerin2009, Sums of products of generalized Fibonacci and Lucas numbers, Demonstratio Math. Vol. XLII No 2 (2009), gen>

ChaouiMoulineRachidi2002, Application of Markov chains properties to ∞-generalized Fibonacci sequences, Fibonacci Quart. 2002 (40,5): 453-459, fibqy>

Church Jr.1974, Lattice paths and Fibonacci and Lucas numbers, Fibonacci Quart. 1974 (12,4): 336-338, fibqy>

Cigler2003, q-Fibonacci polynomials, Fibonacci Quart. 2003 (41,1): 31-40, fibqy>

CvetkovicRajkovicIvkovic2002, Catalan numbers, the Hankel transform, and Fibonacci numbers, J. Integer Seq. Vol. 5 (2002), Article 02.1.3, jis>

de AndradeSantosda SilvaSilva2013, Polynomial generalizations and combinatorial interpretations for seq. including the Fibonacci and Pell numbers, Open J. of Discrete Math. 2013, 3, 25-32, gen>

deBruijn1974, An extension of Fibonacci's sequence, Fibonacci Quart. 1974 (12,3): 251-258, fibqy>

DeCarli1970a, A generalized Fibonacci sequence over an arbitrary ring-Part I, Fibonacci Quart. 1970 (8,2): 182-184, fibqy>

DeCarli1970b, A generalized Fibonacci sequence over an arbitrary ring-Part II, Fibonacci Quart. 1970 (8,2): 198, fibqy>

Dilcher2000, Hypergeometric functions and Fibonacci numbers, Fibonacci Quart. 2000 (38,4): 342-363, fibqy>

Djordjevic2001a, Some properties of partal derivatives of generalized Fibonacci and Lucas polynomials, Fibonacci Quart. 2001 (39,2): 138-141, fibqy>

Djordjevic2005b, On the kth–order derivative sequences of generalized Fibonacci and Lucas polynomials, Fibonacci Quart. 2005 (43,4): 290-298, fibqy>

Djordjevic2009, Generalizations of the Fibonacci and Lucas polynomials, Filomat 23:3 (2009), 291-301, gen>

DresdenDu2014, A simplified Binet formula for k-generalized Fibonacci numbers, J. Integer Seq. Vol. 17 (2014), Article 14.4.7, jis>

Dubeau1993, The rabbit problem revisited, Fibonacci Quart. 1993 (31,3): 268-273, fibqy>

EdsonYayenie2009, A new generalization of Fibonacci sequence and extended Binet's formula, Integers 9 (2009), 639-654, gen>

Elmore1967, Fibonacci functions, Fibonacci Quart. 1967 (5,4): 371-382, fibqy>

Er1984, The matrices of Fibonacci numbers, Fibonacci Quart. 1984 (22,2): 134-139, fibqy>

FalconPlaza2009, On k-Fibonacci sequences and polynomials and their derivatives, Chaos, Solitons and Fractals, Vol. 39, Issue 3, Feb 2009, 1005-1019, gen>

Feinberg1963, Fibonacci-Tribonacci, Fibonacci Quart. 1963 (1,3): 71-74, fibqy>

FengZhang Z.2003, Computational formulas for convoluted generalized Fibonacci and Lucas numbers, Fibonacci Quart. 2003 (vol.41,2): 144-151, fibqy>

Ferns1969, Products of Fibonacci and Lucas numbers, Fibonacci Quart. 1969 (7,1): 1-12, fibqy>

Filipponi1995, Some binomial Fiboancci identities, Fibonacci Quart. 1995 (33,3): 251-257,  fibqy>

Filipponi1996, On the Fibonacci numbers whose subscript is a power, Fibonacci Quart. 1996 (34,3): 271-276,  fibqy>

FilipponiHoradam1993a, Second derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quart. 1993 (31,3): 194-204, fibqy>

FilipponiHoradam1993b(addendum), Addendum to "Second derivative sequences of Fibonacci and Lucas polynomials", Fibonacci Quart. 1993 (31,3): 194-204, fibqy>

Fuller1978, Vectors whose elements belong to a generalized Fibonacci sequence, Fibonacci Quart. 1978 (16,5): 447-450, fibqy>

Gamkrelidze1995, On a probalistic property of the Fibonacci sequence, Fibonacci Quart. 1995 (33,2): 147-152, fibqy>

GarnierRamaré2008-09, Fibonacci numbers and trigonometric identities, Fibonacci Quart. 2008-09 (46-47,1): 56-61, fibqy>

GarthMillsMitchell2007, Polynomials generated by the Fibonacci sequence, J. Integer Seq. Vol. 10 (2007), Article 07.6.8, jis>

Geldenhuys(errata)1982, (errata)On the Fibonacci numbers minus one, Fibonacci Quart. 1982 (20,2): 192, fibqy>

Geldenhuys1981, On the Fibonacci numbers minus one, Fibonacci Quart. 1981 (19,5):  456-457, fibqy>

Gica2008-09, Quadratic residues in Fibonacci sequences, Fibonacci Quart. 2008-09 (46-47,1): 68-72, fibqy>

GodaseDhakne2014, On the properties of k-Fibonacci and k-Lucas numbers, Int. J. Adv. Appl. Math. and Mech. 2 (1) (2014), 100-106, gen>

Good1974, A reciprocal series of Fibonacci numbers, Fibonacci Quart. 1974 (12,4): 346, fibqy>

Gootherts1968a, Linear algebra constructed from Fibonacci sequences Part I: Fundamentals and polynomial interpretations, Fibonacci Quart. 1968 (6,5): 35-42, fibqy>

Gootherts1968b, Linear algebra constructed from Fibonacci sequences Part II: Function sequences and Taylor series of function sequences, Fibonacci Quart. 1968 (6,5): 44-54, fibqy>

Gould1965, Non-Fibonacci numbers, Fibonacci Quart. 1965 (3,3): 177-183, fibqy>

Gould1965_(corrections), Non-Fibonacci numbers, Fibonacci Quart. 1965 (3,3): 184, fibqy>

Gould1981, A history of the Fibonacci Q-matrix and a higher-dimensional problem, Fibonacci Quart. 1981 (19,3): 250-256, fibqy>

GoytSagan2009, Set partition statistics and q-Fibonacci numbers, European J. Combin. Vol. 30, Issue 1, Jan. 2009, 230-245, gen>

GregoryMetzger1978, Fibonacci sine sequences, Fibonacci Quart. 1978 (16,2): 119-120, fibqy>

GulecTaskaraUslu2013, A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients, Appl. Math. Comput. Vol. 220, Sep 2013, 482-486, gen>

GuptaPanwar2012, Common factors of generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers, Int. J. Appl. Math. Research, 1 (4) (2012) 377-382, gen>

GuptaPanwarSikhwal2012a, Generalized Fibonacci sequences, Theoretical Math. and Appl. vol.2, no.2, 2012, 115-124, gen>

GuptaPanwarSikhwal2012b, Generalized Fibonacci-like polynomial and its determinantal identities, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 29, 1415-1420, gen>

Halton1967, Some properties associated with square Fibonacci numbers, The Fibonacci Quarterly 1967 (5,4): 347-354, fibqy>

HarneBadshahSethiya2014, Some identities of Fibonacci like sequences, Int. J. of Math. and Computer Research Vol. 2, issue 3, Mar 2014: 371-374,  gen>

Heberle2012, A combinatorial approach to r-Fibonacci numbers, Harvey Mudd College Department of Math.-Clarement-USA (2012). HMC Senior Theses 34, gen>

Heimer1967, A general Fibonacci function, Fibonacci Quart. 1967 (5,5): 481-483, fibqy>

Heyde1980, On a probabilistic analogue of the Fibonacci sequence, J. Appl. Probab. Vol. 17, No. 4, Dec 1980, 1079-1082,  jou>

Hilton1974, On the partition of Haradam's generalized sequences into generalized Fibonacci and generalized Lucas sequences, Fibonacci Quart. 1974 (12,4): 339-344, fibqy>

HiltonPedersenVrancken1995, On certain arithmetic properties of Fibonacci and Lucas numbers, Fibonacci Quart. 1995 (33,3): 211-217, fibqy>

Hoggatt, Jr.1967, Fibonacci numbers and generalized binomial coefficients, Fibonacci Quart. 1967 (5,4): 383, fibqy>

Hoggatt, Jr.Basin1963a, Representations by complete sequences-Part I (Fibonacci), Fibonacci Quart. 1963 (1,3): 1-14, fibqy>

Hoggatt, Jr.Bicknell1976e, Reciprocal series of Fibonacci numbers with subscripts 2^nk, Fibonacci Quart. 1976 (14,5): 453-454,  fibqy>

Hoggatt, Jr.Bicknell-Johnson1978a, A primer for the Fibonacci numbers XVII: Generalized Fibonacci numbers satisfying u_(n+1)u_(n-1)-u_(n)^2 =±1, Fibonacci Quart. 1978 (16,2): 128-137, fibqy>

Hoggatt, Jr.Bicknell-Johnson1978b, Convolution arrays for Jacobsthal and Fibonacci polynomials, Fibonacci Quart. 1978 (16,5): 385-402,  fibqy>

Hoggatt, Jr.Lind1968, Symbolic substitutions into Fibonacci polynomials, Fibonacci Quart. 1968 (6,5): 55-74, fibqy>

HollidayKomatsu2011, On the sum of reciprocal generalized Fibonacci numbers, Integers 11A (2011) - Proc. of Integers Conference 2009, gen>

Horadam1961, A generalized Fibonacci sequence, Amer. Math. Monthly Vol. 68, No. 5 (May, 1961), 455-459, nat>

HoradamFilipponi1991, Cholesky algorithm matrices of Fibonacci type and properties of generalized sequences, Fibonacci Quart. 1991 (29,2): 164-173, fibqy>

Hosoya1976, Fibonacci triangle, Fibonacci Quart. 1976 (14,2): 173-179, fibqy>

Howard2003, The sum of squares of two generalized Fibonacci numbers, Fibonacci Quart. 2003 (41,1): 80-84, fibqy>

HowardCooper2011, Some identities for r-Fibonacci numbers, Fibonacci Quart. 2011 (49,3): 231-242, fibqy>

IsmailescuSon2014, A new kind of Fibonacci-like sequence of composite numbers, J. of Integer Seq., Vol. 17 (2014), Article 14.8.2, jis>

Iyer1969a, Identities involving generalized Fibonacci numbers, Fibonacci Quart. 1969 (7,1): 66-72, fibqy>

Iyer1969b, Sums involving Fibonacci numbers, Fibonacci Quart. 1969 (7,1): 92-98, fibqy>

Jennings1993, Some polynomial identities for the Fibonacci and Lucas numbers, Fibonacci Quart.  1993 (31,2):  134-137, fibqy>

Jennings1994, On sums of reciprocals of Fibonacci and Lucas numbers, Fibonacci Quart. 1994 (32,1): 18-21, fibqy>

JiaLiuWang2007, q-analogs of generalized Fibonacci and Lucas polynomials, Fibonacci Quart. 2007 (45,1): 26-34, fibqy>

John1984, On the asymptotic proportions of zeros and ones in Fibonacci sequences, Fibonacci Quart. 1984 (22,2): 144-145, fibqy>

Joshi2006, Applications of Fibonacci numbers, J. Int. Acad. Phys. Sci. Vol.10 (2006), 103-112, jou>

Joshi2013, Fibonacci like sequences and characteristic properties, Bull. Marathwada Math. Soc. Vol. 14, No. 2, Dec 2013, 25-34, nat>

Jun S.P.2015, Complex factorizations of the generalized Fibonacci sequences {qn}, Korean J. Math. 23 (2015), No. 3, 371-377, nat>

KaygisizSahin2012a, Determinant and permanent of Hessenberg matrix and Fibonacci type numbers, Gen. Math. Notes Vol. 9, No. 2, April 2012, 32-41, gen>

Kiliç2008, The Binet formula, sums and representations of generalized Fibonacci p-numbers, European J. Combin. Vol. 29, Issue 3, Apr 2008, 701-711, gen>

Kiliç2010, The generalized Fibonomial matrix, European J. Combin. Vol. 31, Issue 1, Jan 2010, 193-209, gen>

Kohler1985, Generating functions of Fibonacci-like sequences and decimal expansions of some fractions, Fibonacci Quart. 1985 (23,1): 29-35, fibqy>

Koshy2011, Fibonacci, Lucas, and Pell numbers, and Pascal’s triangle, Mathematical Spectrum 2010/2011, Vol. 43 Issue 3, 125, gen>

Lang1992, A combinatorial problem in the Fibonacci nb. system and two-variable generalizazions of Chebyshev's polynomials, Fibonacci Quart. 1992 (30,3): 199-210, fibqy>

Lee J-Z.Lee J-S.1988, A note on the generalized Fibonacci numbers, Fibonacci Quart. 1998 (26,1): 14-19, fibqy>

LeeKimLee2002, Factorizations and eignvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart. 2002 (40,3): 203-211, fibqy>

LeeLeeKimShin2001, The Binet formula and representations of k-generalized Fibonacci numbers, Fibonacci Quart. 2001 (39,2): 158-164, fibqy>

Levine1968, Fibonacci sequences with identical characteristic values, Fibonacci Quart. 1968 (6,5): 75-80, fibqy>

Li2014, On Chebyshev polynomials, Fibonacci polynomials, and their derivatives, J. Appl. Math. Vol. 2014, Article ID 451953, 8 p, jou>

Liu2002, Formulas for convolution Fibonacci numbers and polynomials, Fibonacci Quart. 2002 (40,4): 352-357, fibqy>

LiuZhao F-Z.2012, On the sums of reciprocal hyperfibonacci numbers and hyperlucas numbers, J. Integer Seq. Vol. 15 (2012), Article 12.4.5, jis>

Luca2000, Equations involving arithmetic functions of Fibonacci and Lucas numbers, Fibonacci Quart. 2000 (38,1): 49-55, fibqy>

LuJang2013, The sum and product of Fibonacci numbs. and Lucas numbs., Pell numbs. and Pell-Lucas numbs. representation by matrix method, WSEAS Trans. on Math., Issue 4, Vol. 12, Apr 2013, gen>

MansourShattuck2012, Polynomials whose coefficients are k-Fibonacci numbers, Ann. Math. Inform. 40 (2012), p 57-76, nat>

MarquesTrojovsky2012, On divisibility of Fibonomial coefficients by 3, J. Integer Seq. Vol. 15 (2012), Article 12.6.4, gen>

MasonHudson2004, A generalization of Euler's formula and its connection to Fibonacci numbers, Proc. 10th int. Conf. on Fibonacci numbers and their Applic. 2004, Vol. 9, 177-185, gen>

May_1968, On a characterization of the Fibonacci sequence, Fibonacci Quart. 1968 (6,5): 11-14, fibqy>

Melham1999, Sums involving Fibonacci and Pell numbers, Port. Math. Vol. 56 Fasc. 3, 1999, nat>

Melham2000, Sums of certain products of Fibonacci and Lucas numbers-Part II, Fibonacci Quart. 2000 (38,1): 3-7, fibqy>

Melham2003, On some reciprocal sums of Brousseau; an alternative approach to that of Carlitz, Fibonacci Quart. 2003 (41,1): 58-62, fibqy>

Melham2013, Finite sums that involve reciprocals of products of generalized Fibonacci numbers, Integers 13 (2013), gen>

MezňDil2009, Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence, Cent. Eur. J. Math. Jun 2009, Vol. 7, Issue 2, 310-321, gen>

Miles, Jr.1960, Generalized Fibonacci numbers and associated matrices, Amer. Math. Monthly,Vol. 67, No. 8 (Oct., 1960), 745-752, nat>

Monzingo1974a, On extending the Fibonacci numbers to the negative integers, Fibonacci Quart. 1974 (12,3): 292, fibqy>

Monzingo1974b, On extending the Fibonacci numbers to the negative integers (continued I), Fibonacci Quart. 1974 (12,3): 308, fibqy>

Monzingo1974c, On extending the Fibonacci numbers to the negative integers (continued II), Fibonacci Quart. 1974 (12,3): 316, fibqy>

Munarini2005, Generalized q-Fibonacci numbers, Fibonacci Quart. 2005 (43,3): 233-242, fibqy>

Muskat1993, Generalized Fibonacci and Lucas sequences and rootfinding methods, Math. Comp. 61 (1993), 365-372, gen>

NalliHaukkanen2009, On generalized Fibonacci and Lucas polynomials, Chaos, Solitons and Fractals Vol. 42, Issue 5, Dec 2009, 3179-3186, gen>

Nyblom2001, On irrational valued series involving generalized Fibonacci numbers II, Fibonacci Quart. 2001 (39,2): 149-157, fibqy>

Nyblom2003, A non-integer property of elementary symmetric functions in reciprocals of generalized Fibonacci numbers, Fibonacci Quart. 2003 (41,2): 152-155, fibqy>

ÖcalTugluAltinisik2006, On the representation of k-generalized Fibonacci and Lucas numbers, Applied Math. Comp. Vol. 170, Issue 1, 584-596 (Nov 2005), gen>

Ozgur2002, Generalizations of Fibonacci and Lucas sequences, Note di Matematica 21, n. 1, 2002, 113-125, gen>

PanarioSahinWang2013, A family of Fibonacci-like conditional sequences, Integers 13 (2013), gen>

Pandey2013, On some magnified Fibonacci numbers modulo a Lucas number, J. Integer Seq. Vol. 16 (2013), Article 13.1.7, jis>

PanwarRathoreChawla2014, On the k-Fibonacci-like numbers, Turkish J. of Analysis and Number Theory, 2014, Vol. 2, No. 1, 9-12, nat>

PanwarSingh2014a, Generalized bivariate Fibonacci-like polynomials, Int J. of Pure Math. Vol. 1, 2014, gen>

PanwarSingh2014b, Certain properties of generalized Fibonacci sequence, Turkish J. of Analysis and Number Theory 2014, Vol. 2, No. 1, 6-8, nat>

PanwarSingh2014c, k-generalized Fibonacci numbers, Appl. Math. and Physics, 2014, Vol. 2, No. 1, 10-12, gen>

PanwarSinghGupta2013, Generalized Fibonacci polynomials, Turkish J. of Analysis and Number Theory, 2013, Vol. 1, No. 1, 43-47, nat>

PhilippouMakri1985, Longest success runs and Fibonacci-type polynomials, Fibonacci Quart. 1985 (23,4): 338-345, fibqy>

Pla1994, An "All or None" divisibility property for a class of Fibonacci-like sequences of integers, Fibonacci Quart. 1994 (32,3): 226-227, fibqy>

Popov1985, A note on the sums of Fibonacci and Lucas polynomials, Fibonacci Quart. 1985 (23,3): 238-239, fibqy>

Prodinger2009, On the expansion of Fibonacci and Lucas polynomials, J. Integer Seq. Vol. 12 (2009), Article 09.1.6, jis>

Raab1963, A generalization of the connection between the Fibonacci sequence and Pascal's triangle, Fibonacci Quart. 1963 (1,3): 21-31, fibqy>

Rabinowitz1999a, Algorithmic summation of reciprocals of products of Fibonacci numbers, Fibonacci Quart. 1999 (37,2): 122-127, fibqy>

RamirezSirvent2016, A q-analogue of the bi-periodic Fibonacci sequence, J. Integer Seq., Vol. 19 (2016), Article 16.4.6, aXv>

Robbins1994, On Fibonacci numbers and primes of the form 4k + 1, Fibonacci Quart. 1994 (32,1): 15-16, fibqy>

Rudolph-Lilith2016, On the product representation of number sequences, with applications to the family of generalized Fibonacci numbers, J. Integer Seq. Vol. 19 (2016), Article 16.3.6, jis>

SantosIvkovic2005, Polynomial generalizations of the Pell sequences and the Fibonacci sequence, Fibonacci Quart. 2005 (43,4): 328-338, fibqy>

Sburlati2002, Generalized Fibonacci sequences and linear congruences, Fibonacci Quart. 2002 (40,5): 446-452, fibqy>

Sburlati2007, Generalized Fibonacci sequences and linear recurrences, Rend. Sem. Mat. Univ. Pol. Torino - Vol. 65, 3 (2007), nat>

Shannon2010, Another generalization of the Fibonacci and Lucas numbers, Notes Number Theory Discrete Math.16 (2010), 3, 11-17, gen>

Shapiro1976b, Fibonacci numbers and upper triangular groups, Fibonacci Quart. 1976 (14,3): 201-202, fibqy>

ShattuckWagner2007, Some generalized Fibonacci polynomials, J. Integer Seq. Vol. 10 (2007), Article 07.5.3, jis>

ShiuYerger2009, Geometric and Harmonic variations of the Fibonacci sequence, Mathematical Spectrum 2009, gen>

SiarKeskin2013, Some new identities concerning generalized Fibonacci and Lucas numbers, Hacet. J. Math. Stat. Vol. 42 (3) (2013), 211-222, gen>

SilberGellar1976, The algebra of Fibonacci representations, Fibonacci Quart. 1976 (14,4): 289-326, fibqy>

SilvaHoggatt Jr.1980, Generalized Fibonacci numbers, Fibonacci Quart. 1980 (14,4): 290-299, fibqy>

SinghBhatnagarSikhwal2013, Fibonacci-like polynomials and some identities, Int. J. Advanced Math. Sci. 1 (3) (2013) 152-157, gen>

SinghGuptaSikhwal2014, Generalized Fibonacci-like polynomials and some identities, Global J. of Mathematical Analysis, 2 (4) (2014) 249-258, gen>

Smith2008-09, On an `uncounted' Fibonacci identity and its q-analogue, Fibonacci Quart. 2008-09 (46-47,1): 73-78, fibqy>

Sofo2003, Fibonacci and some of his relations, The Math. Educ. into the 21st Century Project - Proc. Int. Conf. Brno, Czech Rep. 2003, gen>

SofoCerone1998b, On a Fibonacci related series, Fibonacci Quart. 1998 (36,3): 211-215, fibqy>

StakhovRozin2006, Theory of Binet formulas for Fibonacci and Lucas p-numbers, Chaos, Solitons and  Fractals, Vol. 27, Issue 5, Mar 2006, 1162-1177, gen>

StanimirovicNikolovStanimirovic2008, A generalization of Fibonacci and Lucas matrices, Discrete Appl. Math. Vol. 156, Issue 14, Jul 2008, 2606-2619, gen>

Stanley1975, The Fibonacci lattice, Fibonacci Quart. 1975 (13,3):  215-232, fibqy>

Stanley1976, Some remarks on the periodicity of the sequence of Fibonacci numbers, Fibonacci Quart. 1976 (14,1): 52-53, fibqy>

Steiner1978, On N-th powers in the Lucas and Fibonacci series, Fibonacci Quart. 1978 (vol.16,5): 451-458, fibqy>

Sun Z-H.Sun Z-W.1992, Fibonacci numbers and Fermat's last theorem, Acta Arith. LX.4 (1992), gen>

Swift2003, Some Fibonacci-like sequences, Appl. Prob. Trust 2003, gen>

TaherMoulineRachidi2002, Convergence of r-generalized Fibonacci sequences and an extension of Ostrowski's condition, Fibonacci Quart. 2002 (40,5): 386-393, fibqy>

Tauber1968a, Lah numbers for Fibonacci and Lucas polynomials, Fibonacci Quart. 1968 (6,5): 93-99, fibqy>

Tauraso2016, Some congruences for central binomial sums involving Fibonacci and Lucas numbers, J. Integer Seq. Vol. 19 (2016), Article 16.5.4, jis>

Tingting W.Wenpeng Z.2012, Some identities involving Fibonacci, Lucas polynomials and their applications, Bull. Math. Soc. Sci. Math. Roumanie Tome 55 (103) No. 1, 2012, 95-103, nat>

Vaughan1976, A note on some arithmetic functions connected with the Fibonacci numbers, Fibonacci Quart. 1976 (14,3): 244-248, fibqy>

Velasco2012, A note on Fibonacci and Lucas and Bernoulli and Euler polynomials, J. Integer Seq. Vol. 15 (2012), Article 12.2.7, jis>

Vince1978, The Fibonacci sequence modulo N, Fibonacci Quart. 1978 (16,5): 403-406, fibqy>

Vinh2007, On Fibonacci-like sequences, J. Integer Seq. Vol. 10 (2007), Article 07.10.2, jis>

Vsemirnov2004, A new Fibonacci-like sequence of composite numbers, J. Integer Seq. Vol. 7 (2004), Article 04.3.7, jis>

Waddill1974, Matrices and generalized Fibonacci sequences, Fibonacci Quart. 1974 (12,4): 381-386, fibqy>

Wall1985, On triangular Fibonacci numbers, Fibonacci Quart. 1985 (23,1): 77-79, fibqy>

WaltonHoradam1974a, Some aspects of generalized Fibonacci numbers, Fibonacci Quart. 1974 (12,3): 241-250, fibqy>

Wang J.1995, On the k^th derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quart. 1995 (33,2): 174-178, fibqy>

Wang W.Wang T.2008a, Identities via Bell matrix and Fibonacci matrix, Discrete Appl. Math. Vol. 156, Issue 14, 28 Jul 2008, 2793-2803, gen>

Williams1975, On Fibonacci numbers of the form k^2 + 1, Fibonacci Quart. 1975 (13,3): 213-214, fibqy>

WitulaSlota2009, δ-Fibonacci numbers, Appl. Anal. Discrete Math. 2009, 3 Issue 2, 310-329, gen>

Wloch2013, Some identities for the generalized Fibonacci numbers and the generalized Lucas numbers, Appl. Math. Comput. Vol. 219, Issue 10, Jan 2013, 5564-5568, gen>

Yayenie2011, A note on generalized Fibonacci sequences, Appl. Math. Comput. Vol. 217, Issue 12, Feb 2011, 5603-5611, gen>

Young1994, p-adic congruences for generalized Fibonacci sequences, Fibonacci Quart. 1994 (32,1): 2-10, fibqy>

YuanHeZhou2014, On the sum of reciprocal generalized Fibonacci numbers, Abstr. Appl. Anal. Vol. 2014 (2014), Article ID 402540, 4 p,  gen>

Zhang G.J.2011, The infinite sum of reciprocal of the Fibonacci numbers, J. Math. Res. Exposition, Nov 2011, Vol. 31, No. 6, 1030-1034, jou>

Zhang T.Ma2005, On generalized Fibonacci polynomials and Bernoulli numbers, J. Integer Seq. Vol. 8 (2005), Article 05.5.3, jis>

Zhang W.1997, Some identities involving the Fibonacci numbers, Fibonacci Quart. 1997 (35,3): 225-229, fibqy>

Zhang W.2002, On Chebyshev polynomials and Fibonacci numbers, Fibonacci Quart. 2002 (40,5): 424-428, fibqy>

Zhang W.2004, Some identities involving the Fibonacci numbers and Lucas numbers, Fibonacci Quart. 2004 (42,2): 149-154, fibqy>

Zhang Z.Wang X.2007, A factorization of the symmetric Pascal matrix involving the Fibonacci matrix, Discrete Appl. Math. Vol. 155, Issue 17, Oct 2007, 2371-2376, gen>

ZhangWu2013, On the reciprocal sums of the generalized Fibonacci sequences, Adv. Difference Equ. 2013, 2013: 377, gen>

Zhao F.2001, Summation of certain reciprocal series related to the generalized Fibonacci and Lucas numbers, Fibonacci Quart. 2001 (39,5): 392-397, fibqy>

Zhao F.Wang T.2001b, Some identities for the generalized Fibonacci and Lucas functions, Fibonacci Quart. 2001 (39,5): 436-438, fibqy>

Zhao Y.2008-09, The coefficients of a truncated Fibonacci power series, Fibonacci Quart. 2008-09 (46-47,1): 53-55, fibqy>

Zhou1996, On the kth-order derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quart. 1996 (34,5): 394-408, fibqy>

Fibonacci-Lucas

Dar2012, Generalized Fibonacci-Lucas sequence, Int. J. of Mathematical Archive-3(6), 2012,  gen>

Ma1998, A generalization of the Kummer identity and its application to Fibonacci-Lucas sequences, Fibonacci Quart. 1998 (36,4): 339-347, fibqy>

SinghSikhwalGupta2014, Generalized Fibonacci-Lucas Sequence, Turkish J. of Analysis and Number Theory, 2014, Vol. 2, No. 6, 193-197, nat>

SinghSikhwalParsaiGupta2014, Generalized Fibonacci-Lucas polynomials, Int. J. Advanced Math. Sci. 2 (1) (2014) 81-87, gen>

Zhang Z.Jin1998, Some identities involving generalized Genocchi polynomials and generalized Fibonacci-Lucas sequences, Fibonacci Quart. 1998 (36,4): 329-334, fibqy>

Zhou2003, Applications of matrix theory to congruence properties of kth-order F-L sequences, Fibonacci Quart. 2003 (41,1): 48-58, fibqy>

Fibonomial coefficients

AmdeberhanChenMollSagan2014, Generalized Fibonacci polynomials and Fibonomial coefficients, Ann. Comb. (2014) Vol.18, Issue 4: 541-562, gen>

BenjaminPlott2008-2009, A combinatorial approach to fibonomial coefficients, Fibonacci Quart. 2008-09 (46-47,1): 7-9, fibqy>

BenjaminQuinnRouse2004, Fibinomial identities, Proc. of the 10th Int. Conf. on Fibonacci nbs. and their Appl. 2004, Vol. 9, 19-24, gen>

Kiliç2010, The generalized Fibonomial matrix, European J. Combin. Vol. 31, Issue 1, Jan 2010, 193-209, gen>

Marques2012, Fibonomial coefficients at most one away from Fibonacci numbers, Demonstratio Math. Vol. XLV No 1 2012, gen>

SeibertTrojovsky2005, On some identities for the Fibonomial coefficients, Math. Slovaca, Vol. 55 (2005), No. 1, 9-19, nat>

TugluYesilKocerDziemianczuk2014, The -analogue of Riordan representation of Pascal matrices via fibonomial coefficients, J. Appl. Math. Vol. 2014 (2014), Article ID 841826, 6 p, jou>

Velasco2011, On s-fibonomials, J. Integer Seq. Vol. 14 (2011), Article 11.3.7, jis>

Fine

DeutschShapiro2001, A survey of the Fine numbers, Discrete Math. Vol. 241, Issues 1–3, 28 Oct 2001, 241-265, gen>

Frobenius

KimKimRimDolgy2013b, Some identities of Frobenius-type Eulerian polynomials arising from umbral calculus, Int. J. Math. Anal. (Ruse), Vol. 7, 2013, no. 53, 2637-2644, gen>

KimMansour2014, Umbral calculus associated with Frobenius-type Eulerian polynomials, Russ. J. Math. Phys. Jun 2014, Vol. 21, Issue 4, 484-493, nat>

ShallitStakowicz2011, Unbounded discrepancies in Frobenious numbers, Integers 11.1 (2011): 27-34, gen>

Gandhi

HanZeng1999a, q-polynômes de Gandhi et statistique de Denert, Discrete Math. Vol. 205, Issues 1–3, 28 July 1999, 119-143, gen>

Gauss (see also hypergeometric)

AhmiaBelbachirBelkhir2014, The log-concavity and log-convexity properties associated to hyperPell and hyperPell-Lucas sequences, Ann. Math. Inform. 43 (2014) 3-12, gen>

BahsiMezoSolak2014, A symmetric algorithm for hyper-Fibonacci and hyper-Lucas numbers, Ann. Math. Inform. 43 (2014), 19-27, gen>

BelbachirBelkhir2014, Combinatorial expressions involving Fibonacci, hyperfibonacci, and incomplete Fibonacci numbers, J. Integer Seq. Vol. 17 (2014), Article 14.4.3, aXv>

Ben CheikhOuni2008, Some generalized hypergeometric d-orthogonal polyn. sets, J. Math. Anal. Appl. Vol. 343, Issue 1, Jul 2008, 464-478, jou>

Berndt2000, Flowers which we cannot yet see growing in Ramanujan’s garden of hypergeometric series, elliptic functions, and q ’s, Nato Sci. Ser. II Math. Phys. Chem. Vol. 30, 2001, 61-85, gen>

Beukers2009, Gauss hypergeometric function, Vol. 260 of Progress in Mathematics, 23-42, gen>

ByrnesJiuMollVignat2013, Recursion rules for the hypergeometric zeta function, arXiv (8 May 2013), aXv>

CaoZhao F-Z.2010, Some properties of hyperFibonacci and hyperLucas numbers, J. Integer Seq. Vol. 13 (2010), Article 10.8.8, jis>

ChanChenSrivastava2002, Certain classes of generating functions for the Jacobi and related hypergeometric polynomials, Comput. Math. Appl. Vol. 44, Issue 12, Dec 2002, 1539-1556, gen>

ChenSrivastava1995, Orthogonality relations and generating functions for Jacobi polynomials and related hypergeometric functions, Appl. Math. Comput. Vol. 68, Issues 2–3, 15 Mar 1995, 153-188, gen>

Chu1997a, Hypergeometric series and the Riemann zeta function, Acta Arith. LXXXII.2 (1997), gen>

Chu2002, Inversion techniques and combinatorial identities: balanced hypergeometric series, Rocky Mountain J. Math. Vol. 32, No. 2 (2002), 561-588, nat>

CohlMacKenzieVolkmer2013, Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals, J. Math. Anal. Appl. Vol. 407, Issue 2, Nov 2013, 211-225, jou>

Dilcher2000, Hypergeometric functions and Fibonacci numbers, Fibonacci Quart. 2000 (38,4): 342-363, fibqy>

EhrenborgReaddy2016, The Gaussian coefficient revisited, J. Integer Seq. Vol. 19 (2016), Article 16.7.8, jis>

HassenNguyen2005, Hypergeometric zeta functions, arXiv (27 Sep 2005), aXv>

HassenNguyen2008, Hypergeometric Bernoulli polynomials and Appell sequences, Int. J. Number Theory, Vol. 04, Issue 05, Oct 2008, gen>

KoekoekLeskySwarttouw2013, Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics 2013, gen>

Koornwinder1988, Group theoretic interpretation of Askey's scheme of hypergeometric orthogonal polynomials, Lecture Notes in Math. Vol. 1329, 1988, 46-72, gen>

Koornwinder2014, Additions to the formula lists in "Hypergeometric orthogonal polynomials and their q-analogues" by Koekoek, Lesky and Swarttouw, arXiv (4 Jan 2014), aXv>

KoornwinderOnn2006, LU factorizations, q = 0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials, Ramanujan J. Vol. 13, Issue 1-3, (Jun 2007), 365-387, aXv>

LahiriSatyanarayana1995, Certain bilateral generating relations for generalized hypergeometric functions, Proc. Indian Acad. Sci. Math. Sci. (Aug 1995) Vol. 105, Issue 3, 297-301, nat>

LiuWang W.2012, Harmonic number identities via hypergeometric series and Bell polynomials, Integral Transforms Spec. Funct. Vol. 23, Issue 1, 2012, gen>

LiuZhao F-Z.2012, On the sums of reciprocal hyperfibonacci numbers and hyperlucas numbers, J. Integer Seq. Vol. 15 (2012), Article 12.4.5, jis>

LouckBiedenharn1977, A generalization of the Gauss hypergeometric series, J. Math. Anal. Appl. Vol. 59, Issue 3, Jul 1977, 423-431, jou>

MubeenRahmanRehmanNaz2014, Contiguous function relations for k-hypergeometric functions, Mathematical Analysis Vol. 2014 (2014), Article ID 410801, 6 p, gen>

Neuschel2012, Asymptotics for ménage polynomials and certain hypergeometric polynomials of type 3F1, J. Approx. Theory 164 (2012) 981-1006, jou>

PandaSrivastava1976, Some bilateral generating functions for a class of generalized hypergeometric polynomials, Journal für die reine und angewandte Mathematik Vol. 1976, Issue 283-284, 265-274, nat>

SatyanarayanaSrimannarayanaKumar2014, Certain bilateral generating relations for a class of generalized hypergeometric functions of two variables, Universal Journal of Applied Mathematics 2(1): 5-9, 2014, gen>

Soria-LorenteCumbrera-Gonzales2014, q-hypergeometric representations of the q-analogue of zeta function, J. of Fractional Calculus and Applications Vol. 5 (2) Jul 2014, 1-8, jou>

Vidünas2009, Specialization of Appell’s functions to univariate hypergeometric functions, arXiv(17 Oct 2009), aXv>

Gegenbauer (see also ultraspherical)

Anshelevich2011, A characterization of ultraspherical polynomials, arXiv (3 Aug 2011), aXv>

AskeyKoornwinderRahman1986, An integral of products of ultraspherical functions and q-extensions, J. Lond. Math. Soc. (2) (1986) 33 (1): 133-148, nat>

Chatterjea1969, Bilateral generating function for the ultraspherical polynomials, Pacific J. Math. Vol. 29, No. 1 (1969), 73-76, nat>

Demni2009, Ultraspherical type generating functions for orthogonal polynomials, Probab. Math. Statist. Vol. 29, Fasc. 2 (2009), 281-296, gen>

GouldHe2013, Characterization of (c)-Riordan arrays, Gegenbauer-Humbert-type polynomial sequences, and (c)-Bell polynomials, J. Mathematical Research with Appl. Sept., 2013, Vol. 33, No. 5, 505-527, jou>

GrozaKachuryk2006, On orthogonality relations for dual discrete q-ultraspherical polynomials, SIGMA Symmetry Integrability Geom. Methods Appl. Vol. 2 (2006), Paper 034, 8 p, gen>

Horadam1985, Gegenbauer polynomials revisited, Fibonacci Quart. 1985 (23,4): 294-299, fibqy>

HoradamPethe1981, Polynomials associated with Gegenbauer polynomials, Fibonacci Quart. 1981 (19,5): 393-397, fibqy>

KhanAsif2012, Jacobi type and Gegenbauer type generalization of certain polynomials, Mat. Vesnik, 64, 2 (2012), 147-158, Jun 2012, nat>

Koelink1995, Identities for q-ultraspherical polynomials and Jacobi functions, Proc. Amer. Math. Soc. 123 (1995), 2479-2487, nat>

Koornwinder1990, Jacobi functions as limit cases of q-ultraspherical polynomials, J. Math. Anal. and Appl. Vol. 148, Issue 1 (May 1990) 44–54, jou>

Nagel1994, The relativistic Hermite polynomial is a Gegenbauer polynomial, J. Math. Phys. 35, 1549 (1994), jou>

PacharoniZurrian2014, Matrix ultraspherical polynomials: the 2 × 2 fundamental cases, arXiv (31 may 2014), aXv>

Yasmin2014, Some properties of generalized Gegenbauer matrix polynomials, Int. J. of Analysis Vol. 2014 (2014), Article ID 780649, 12 p, gen>

Gegenbauer-Humbert

He2011b, Characterizations of orthogonal generalized Gegenbauer-Humbert polynomials and orthogonal Sheffer-type polynomials, J. Comput. Anal. Appl. 13.4 (2011): 701-723, jou>

HeShiueWeng2011, Sequences of numbers meet the generalized Gegenbauer-Humbert polynomials, Inter. Scholarly Research Network, Vol. 2011, Article ID 674167, 16 p, gen>

generating functions

AgarwalTariboonJain2014, New bilateral type generating function associated with I-function, Abstr. Appl. Anal. Vol. 2014 (2014), Article ID 157297, 3 p, gen>

AgrawalChaubey1981, Bilateral generating relations for a function defined by generalized Rodrigues formula, Indian J. Pure Appl. Math. 12(3): 377-379, Mar 1981, nat>

AharmimHamyaniWassouliGhanmi2013, New operational formulas and generating functions for the generalized Zernike polynomials, arXiv (12 Dec 2013), aXv>

AlamChongdar2007, On generating functions of modified Laguerre polyn., Rev. Real Academia de Ciencias, Zaragoza 62: 91–98, (2007), nat>

AtakishiyevaAtakishiyev2011, A non-standard generating function for continuous dual q-Hahn polynomials, Revista de Matema'tica: Teorı'a y Aplicaciones Vol. 18 (1): 111-120, Jan 2011, nat>

BabusciDattoliGorskaPenson2012, Generating functions for Laguerre polynomials: new identities for Lacunary Series, arXiv (13 Oct 2012), aXv>

BarberoSalasVillasenior2013, Bivariate generating functions for a class of linear recurrences. II. Applications, arXiv (22 jul 2013), aXv>

BeraChongdar2013, On an extension of bilateral gfs of modified Jacobi polyn. from the existence of partial-quasi bilinear gf, Int. J. Math. Anal. Vol. 7, 2013, no. 35, 1743-1749, gen>

Brafman1951, Generating functions of Jacobi and related polynomials, Proc. Amer. Math. Soc. (1951) xxxx, nat>

Buschman1965, A generating function for Fibonacci numbers, Fibonacci Quart. 1965 (3,3): 199-200, fibqy>

Callan2007, On generating functions involving the square root of a quadratic polynomial, J. Integer Seq. Vol. 10 (2007), Article 07.5.2, jis>

Carlitz1968c, Some generating functions for Laguerre polynomials, Duke Math. J. Vol. 35, Number 4 (1968), 825-827, gen>

Carlitz1969, Generating functions, Fibonacci Quart. 1969 (7,4): 359-393, Carlitz1975b, Note on some generating functions, Fibonacci Quart. 1975 (13,2): 129-133, fibqy>

ChanChenSrivastava2002, Certain classes of generating functions for the Jacobi and related hypergeometric polynomials, Comput. Math. Appl. Vol. 44, Issue 12, Dec 2002, 1539-1556, gen>

ChandraSamantaBera2013, On bilateral generating functions of extended Jacobi polynomials, Int. J. Contemp. Math. Sci. Vol. 8, 2013, no. 20, 1001-1005, gen>

Chatterjea1962, On a generating function of Laguerre polynomials, Boll. Unione Mat. Ital. Serie 3, Vol. 17 (1962), n.2, 179-182, nat>

Chatterjea1969, Bilateral generating function for the ultraspherical polynomials, Pacific J. Math. Vol. 29, No. 1 (1969), 73-76, nat>

Chen2007, Inversion of generating functions using determinants, J. Integer Seq. Vol. 10 (2007), Article 07.10.5, jis>

ChenSrivastava1995, Orthogonality relations and generating functions for Jacobi polynomials and related hypergeometric functions, Appl. Math. Comput. Vol. 68, Issues 2–3, Mar 1995, 153-188, gen>

Chongdar1992, On certain bilateral generating functions, Rend. Istit. Mat. Univ. Trieste vol. XXIV (I-II) 1992, 73-79, nat>

ChuVicenti2003, Funzione generatrice e polinomi incompleti di Fibonacci e Lucas, Boll. Unione Mat. Ital. Serie 8, Vol. 6-B (2003), n.2, 289-308, nat>

Cohen1976, Generating functions for the Jacobi polynomial, Proc. Amer. Math. Soc. Vol. 57, No. 2, Jun 1976, nat>

Cohen1977, Some classes of generating functions for the Laguerre and Hermite polynomials, Math. Comp. Vol. 31, No. 238, Apr 1977, 511-518, gen>

CohenSun1981, On some extensions of the Meixner-Weisner generating functions, Fibonacci Quart. 1981 (19,5): 422-425, fibqy>

CohlMacKenzieVolkmer2013, Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals, J. Math. Anal. Appl. Vol. 407, Issue 2, Nov 2013, 211-225, jou>

Cossali2003, A common generating function for Catalan numbers and other integer sequences, J. Integer Seq. Vol. 6 (2003), Article 03.1.8, jis>

DasChongdar2011, On bilateral generating functions of modified Jacobi polynomials by group theoretic method, J. of Science and Arts Year 11, No. 4(17), 417-424, 2011, jou>

 DattoliLorenzuttaSacchetti2001, Multivariable Lagrange expansion and generalization of Carlitz–Srivastava mixed generating functions, J. Math. Anal. Appl. Vol. 257, Issue 2, May 2001, 308-320, jou>

DattoliMiglioratiSrivastava2004, Some families of generating functions for the Bessel and related functions, Georgian Math. J. Vol. 11 (2004), No. 2, 219-228, nat>

Demni2009, Ultrasherical type generating functions for orthogonal polynomials, Probab. Math. Statist. Vol. 29, Fasc. 2 (2009), 281-296, gen>

DesaleQashash2011, A general class of generating functions of Laguerre polynomials, J. Inequal. Spec. Funct. Vol. 2, Issue 2, 1-7, gen>

DesaleQashash2011a, Trilateral Generating Function for Hermite, Jacobi and Bessel Polyn., Int. Journal of Math. Analysis, Vol. 5, 2011, no. 47, 2329 - 2335,  jou>

Djordjevic2004, Generating functions of the incomplete generalized Fibonacci and generalized Lucas numbers, Fibonacci Quart. 2004 (42,2): 106-113, fibqy>

FoataLeroux1983, Polynômes de Jacobi, interprétation combinatoire et fonction génératrice, Proc. Amer. Math. Soc. Vol. 87, No. 1 (Jan-Apr, 1983), 47-53, nat>

FlajoletGardyGouyou-Beauchamps2004, Generating functions for generating trees, arXiv (11 Nov 2004), aXv>

Fray1967, A generating function associated with the generalized Stirling numbers, Fibonacci Quart. 1967 (5,4): 356-366, fibqy>

GabouryTremblay2014, A further investigation of generating functions related to pairs of inverse functions with appl. to generalized degenerate Bernoulli polyn., Bull. Korean Math. Soc. 51 (2014), No. 3, 831-845, nat>

GetuShapiroWoanWoodson1992, How to guess a generating function, SIAM J. Discrete Math. Vol. 5 Issue 4, Nov. 1992, 497-499, gen>

GoginHirvensalo2007, On the generating function of discrete Chebyshev polynomials, Turku Centre for Computer Science, TUCS Technical Report No 819, Apr 2007, nat>

Griffiths2014, Generating functions for extended Stirling numbers of the first kind, J. Integer Seq. Vol. 17 (2014), Article 14.6.4, jis>

Hansen1972, Generating identities for Fibonacci and Lucas triples, Fibonacci Quart. 1972 (10,6): 571-578, fibqy>

Henrici1955, On generating functions for the Jacobi polynomial, Pacific J. Math. 5 (1955), no. 2, 923-931, nat>

Howard1996, Sums of powers of integers via generating functions, Fibonacci Quart. 1996 (34,3): 244-256, fibqy>

HubbellSrivastava1990, Certain theorems on bilateral generating functions involving Hermite, Laguerre, and Gegenbauer polynomials, J. Math. Anal. Appl. Vol. 152, Issue 2, Nov. 1990, 343-353, jou>

HussainSingh1979, Mixed generating relations for polyn. related to Konhauser biorthogonal polynomials, Port. Math. 1979, Vol. 38, Issue: 3-4, 181-187, nat>

IsmailRashed1977, Polynomials expansions and generating functions, J. Math. Anal. Appl. Vol. 57, Issue 3, Sep 1963 1977, 457-477, gen>

KamarujjamaHussainAftab1997, On partly bilateral and partly unilateral generating relations, Soochow J. Math. Vol. 23, No. 4, 359-363, Oct 1997,

Kar1996, On a general class of generating functions involving modified Bessel polynomials, Bulletin Calcutta Math. Soc. Vol. 88, No. 5, Oct 1996, Article No. 51, 363-366, nat>

KarandeThakare1973, A note on the generating function of Laguerre polynomials, Current Sci. 1973 (42,15): 531, gen>

KidaUrata2013, Involutions on generating functions, J. Integer Seq. Vol. 16 (2013), Article 13.1.6, jis>

KiliçProdinger2014, A note on the conjecture of Ramirez and Sirvent, J. of Integer Seq. Vol. 17 (2014), Article 14.5.8, jis>

Kruchinin D.Kruchinin V.2012, A method for obtaining generating functions for central coefficients of triangles, J. Integer Seq., Vol. 15 (2012), Article 12.9.3, jis>

LahiriSatyanarayana1995, Certain bilateral generating relations for generalized hypergeometric functions, Proc. Indian Acad. Sci. Math. Sci. (Aug 1995) Vol. 105, Issue 3, 297-301, nat>

Lang2002, On polynomials related to derivatives of the generating functions of Catalan numbers, Fibonacci Quart. 2002 (40,4): 299-312, fibqy>

Lee P-A.1997, Probability distribution and a generating function of Laguerre polynomials, Bull. Inst. Math. Acad. Sin. (N.S.), nat>

LinTuSrivastava2001, New generating functions for a class of generalized Hermite polynomials, J. Math. Anal. and Appl. 261, Issue 2, Sep 2001, 479-496, jou>

MahonHoradam1987b, Ordinary generating functions for Pell polynomials, Fibonacci Quart. 1987 (25.1): 45-56, fibqy>

Manocha1967, Some bilinear generating functions for Jacobi polynomials, Math. Proc. Cambridge Philos. Soc. Vol. 63, Issue 02, Apr 1967, 457-459, nat>

ManochaSharma1967, Generating functions of Jacobi polynomials, Math. Proc. Cambridge Philos. Soc. Vol. 63, Issue 02, Apr 1967, 431-433, nat>

Mansour2004a, A formula for the generating functions of powers of Horadam’s sequence, Australas. J. Combin. Vol. 30 (2004), 207-212, nat>

Mittal1972, Polynomials defined by generating functions, Trans. Amer. Math. Soc. Vol. 168, Jun 1972, 73-84, nat>

Mukherjee1996, Generating functions on extended Jacobi polynomials from Lie group view point, Publ. Mat. Vol 40 (1996), 3-13, gen>

Mukherjee2002, An extension of bilateral generating function of certain special function-II, Rev. Real Academia de Ciencias. Zaragoza. 57: 143-146, (2002), nat>

MunotMathur1982, On a multilateral generating function for the extended Jacobi polynomials, Indian J. Pure Appl. Math. 13(5): 597-600, May 1982, nat>

NkwantaTefera2013, Curious relations and identities involving the Catalan generating function and numbers, J. of Integer Seq. Vol. 16 (2013), Article 13.9.5, jis>

ÖnerDanisTurkunHatinogluXXXX, Other generating functions, Math 543 Bonus Project 1-Bilkent Univ. (Ankara) Turkey, gen>

pahio2013, Generating function of Laguerre polynomials, xxxx, xxxx>

PandaSrivastava1976, Some bilateral generating functions for a class of generalized hypergeometric polynomials, Journal für die reine und angewandte Mathematik Vol. 1976, Issue 283-284, 265–274, nat>

PatilThakare1976a, New operational formulas and generating functions for Laguerre polynomials, Indian J. Pure Appl. Math. 1976 (7,10): 1104-1118, nat>

PatilThakare1976b, Some generating functions in unified form for the classical orthogonal polynomials and Bessel polynomials, Indian J. Pure Appl. Math. 1976 (8,1): 94-102, nat>

PatilThakare1977, Bilateral generating function for a function defined by generalized Rodrigue's formula, Indian J. Pure Appl. Math. 1977 (8,4): 425-429, nat>

PeartWoan2000a, Generating functions via Hankel and Stieltjes matrices, J. Integer Seq. Vol. 3 (2000), Article 00.2.1, jis>

PintérSrivastava1999, Generating functions of the incomplete Fibonacci and Lucas numbers, Rend. Circ. Mat. Palermo (2), Tomo XLVII! (1999), 591-596, nat>

Shannon1974b, A method of Carlitz applied to the kth power generating function for Fibonacci numbers, Fibonacci Quart. 1974 (12,3): 293-299, fibqy>

ShuklaMeher2010, Generating functions for Laguerre type polynomials of two variables Ln^(a-n)(x,y) by using group theoretic method, Int. J. Math. Anal. (Ruse), Vol. 4, 2010, no. 48, 2357-2366, gen>

Simsek2013a, Generating function for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications, Fixed Point Theory Appl. 2013, 2013: 87, gen>

SinghalSrivastava1972, A class of bilateral generating functions for certain classical polyn., Pacific J. Math. Volume 42, Number 3 (1972), 755-762, nat>

Srivastava1969a, Some bilinear generating functions, Proc. Natl. Acad. Sci. USA Vol. 64, No. 2 (Oct. 15, 1969), 462-465, nat>

Srivastava1969b, Generating functions for Jacobi and Laguerre polynomials, Proc. Amer. Math. Soc. 23 (1969), 590-595, nat>

Srivastava1974, Note on certain generating functions for Jacobi and Laguerre polynomials, Publications de l'Institut Mathématique 31 (1974): 149-154, nat>

Srivastava1980, Some bilateral generating functions for a certain class of special functions. I l, Indagationes Mathematicae (Proceedings) Vol. 83, Issue 2, 1980, 234-246, gen>

SrivastavaLavoie1975, A certain method of obtainiing bilateral generating functions, Mathematics Indagationes Mathematicae (Proceedings) Vol. 78, Issue 4, 1975, 304-320, gen>

SrivastavaSingh1979b, Some generating relations connected with a function defined by a generalized Rodrigues formula, Indian J. Pure Appl. Math. 10 (10): 1312-1317, Oct 1979, nat>

SrivastavaSinghSingh1979, Operational derivation of generating functions of a generalized function, Indian J. Pure Appl. Math. 10 (3), 326-328, Mar 1979, nat>

SrivastavaSinghSingh1980, Bilateral generating functions for a new class of generalized Legendre polynomials, Int. J. Math. Math. Sci. Vol. 3, No. 2 (1980), 305-310, gen>

SrivastavaYeh2002, Certain theorems on bilinear and bilateral generating functions, Anziam J. 43 (2002), 567-574, gen>

ThakareMadhekar1982, Use of Hermite's method to obtain generating functions for classical orthogonal polynomials, Indian J. Pure Appl. Math. 13(2): 183-189, Feb 1982, nat>

Thakurta1987, Some generating functions of Laguerre polynomials, Int. J. Math. Math. Sci. Vol. 10, No.3 (1987), 531-534, gen>

WanZudilin2011, Generating functions of Legendre polynomials: A tribure to Fred Brafman, xxxx, gen>

Watanabe2010, Symmetry in generating functions, Symmetry 2010, 2, 346-365, gen>

Yang S.Srivastava1997, Some families of generating functions for the Bessel polynomials, J. Math. Anal. Appl. Vol. 211, Issue 1, Jul 1997, 314-325, jou>

Zudilin2014, A generating function of the squares of Legendre polynomials, Bull. Austral. Math. Soc. 89:1 (2014) 125-131 arXiv (4 dec 2012), aXv>

Genocchi

Agoh2014, Convolution identities for Bernoulli and Genocchi polynomials, Electron. J. Combin. 21 (1) (2014),  gen>

AraciAcikgozQi2013, On the q-Genocchi numbers and polyn. with weight zero and their applications, Nonlinear Funct. Anal. Appl. Vol. 18, No. 2 (2013), 193-203,  gen>

AraciAcikgozSen2014a, Some new formulae for Genocchi numbers and polynomials Involving Bernoulli and Euler polynomials, Int. J. Math. Math. Sci. Vol. 2014 (2014), Article ID 760613, 7 p,  gen>

AraciBagdasaryanAgyuzAcikgoz2013, On the modified q-Genocchi numbers and polynomials and their applications, arXiv (23 Nov 2013), aXv>

AraciSenAcikgoz2014, Theorems on Genocchi polynomials of higher order arising from Genocchi basis, Taiwanese J. Math. Vol. 18, No. 2, 473-482, 2014,  nat>

DereSimsek2011b, Genocchi polynomials associated with the umbral algebra, Appl. Math. Comput. Vol. 218, Issue 3, Oct 2011, 756-761,  gen>

Domaratzki2004, Combinatorial interpretations of a generalization of the Genocchi numbers, J. Integer Seq. Vol. 7 (2004), Article 04.3.6,  jis>

DumontFoata1976, Une propriété de symétrie des nombres de Genocchi, Bulletin de la S. M. F., tome 104 (1976), 433-451,  nat>

DumontRandrianarivony1994, Dérangements et nombres de Genocchi, Discrete Math. Vol. 132, Issues 1–3, Sep 1994, 37-49,  gen>

Gandhi1970, A conjectured representation of Genocchi numbers, Amer. Math. Monthly, Vol. 77, No.5, (may 1970), 505-506,  nat>

GuoQi2015a, A new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers, Global J. of Mathematical Anal. 3 (1) (2015) 33-36,  gen>

HanZeng1999b, On a q-sequence that generalizes the median Genocchi numbers, Ann. Sci. Math. Québec 23 (1999), no. 1, 63-72,  gen>

Horadam1992a, Negative order Genocchi polynomials, Fibonacci Quart. 1992 (30,1): 21-34,  fibqy>

Horadam1992b, Generation of Genocchi polynomials of first order by recurrence relations, Fibonacci Quart. 1992 (30,3): 239-242, fibqy>

Kim2013, Some identities on the Bernstein and q-Genocchi polynomials, Bull. Korean Math. Soc. 50 (2013), No. 4, 1289-296,  nat>

KimKurtKurt2013, Some identities on the generalized q-Bernoulli, q-Euler, and q-Genocchi polynomials, Abstr. Appl. Anal. Vol. 2013, Article ID 293532, 6 p,  gen>

Kurt2014, New identities and relations derived from the generalized Bernoulli polynomials, Euler polynomials and Genocchi polynomials, Adv. Difference Equ. 2014, 2014: 5,  gen>

KurtCenkci2010, A new approach to q-Genocchi numbers and polynomials, Bull. Korean Math. Soc. 47 (2010), No. 3, 575-583,  nat>

LiuWang W.2009, Some identities on the Bernoulli, Euler and Genocchi polynomials via power sums and alternate power sums, Discrete Math. Vol. 309, Issue 10, 28 May 2009, 3346-3363,  gen>

Luo2009a, Fourier expansions and integral representations for Genocchi polynomials, J. Integer Seq., Vol. 12 (2009), Article 09.1.4,  jis>

Mahmudov2012b, q-analogues of the Bernoulli and Genocchi polynomials and the Srivastava-Pintér addition theorems, Discrete Dyn. Nat. Soc. Vol. 2012 (2012), Article ID 169348, 8 p,  gen>

MahmudovMomemzadeh2014, On a class of q-Bernoulli, q-Euler and q-Genocchi polynomials, arXiv (18 Jan 2014),  aXv>

Ozarslan2013, Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials, Adv. Difference Equations 2013, 2013: 116,  gen>

ParkKim2008, On some arithmetical properties of the Genocchi numbers and polynomials, Adv. Difference Equ. Vol. 2008, Article ID 195049, 14 p,  gen>

RimJeongLee2012, Identities on the Bernoulli and Genocchi numbers and polynomials, Int J. Math. Mathematical Sciences. Vol. 2012 (2012), Article ID 184649, 9 p, gen>

RimParkMoon2008, On Genocchi numbers and polynomials, Abstr. Appl. Anal. Vol. 2008 (2008), Article ID 898471, 7 p, gen>

Rogala2008, Generalization of the Genocchi numbers to their q-analogue, Honor Theses, 1980, Dept. of Mathematics-Ithaca College, gen>

SimsekCangulKurtKim2008, q-Genocchi numbers and polynomials associated with q-Genocchi-type l-functions, Adv. Difference Equ. 2008, 2008: 815750,  gen>

Srivastava2011, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inf. Sci. 5 (3) (2011), 390-444,  gen>

Zeng J.1996, Sur quelques propriétés de symétrie des nombres de Genocchi, Discrete Math. 153 (1996) 319-333,  gen>

Zeng J.Zhou J.2006, A q-analog of the Seidel generation of Genocchi numbers, European. J. Combin. Vol. 27, Issue 3, Apr 2006, 364-381, gen>

Zhang Z.Jin1998, Some identities involving generalized Genocchi polyn. and generalized Fibonacci-Lucas sequences, Fibonacci Quart. 1998 (36,4): 329-334,  fibqy>

Hahn

AtakishiyevaAtakishiyev2011, A non-standard generating function for continuous dual q-Hahn polynomials, Revista de Matema'tica: Teorı'a y Aplicaciones Vol. 18 (1): 111-120, Jan 2011, nat>

GriffithsSpano2011, Multiv. Jacobi and Laguerre polynomials, infinite-dimens. extensions and their prob. connect. with multiv. Hahn and Meixner polynomials, Bernoulli 17 (3), 2011, 1095-1125, gen>

GroeneveltKoelinkRosengren2003, Continuous Hahn functions as Clebsch-Gordan coefficients, arXiv (20 Feb 2003), aXv>

Koelink1996, On Jacobi and continuous Hahn polynomials, Proc. Amer. Math. Soc. 124 (1996), 887-898, nat>

Hahn's theorem

KwonYoon2000, Generalized Hahn's theorem, J. Comput. Appl. Math. Vol. 116, Issue 2, 15 Apr 2000, 243-262, jou>

Hankel

AndrewsWimp2002, Some q-orthogonal polynomials and related Hankel determinants, Rocky Mountain J. Math. Vol. 32, No. 2, Summer 2002,  nat>

BarryHennessy2010a, The Euler-Seidel matrix, Hankel matrices and moment sequences, J. Integer Seq. Vol. 13 (2010), Article 10.8.2, jis>

BasorChenWidom2001, Determinants of Hankel matrices, J. Funct. Anal. 179, 214-234 (2001), jou>

CameronYip2011, Hankel determinants of sums of consecutive Motzkin numbers, Linear Algebra Appl Vol. 434, Issue 3, 1 Feb 2011, 712-722, gen>

Fasino1995, Spectral properties of Hankel matrices and numerical solutions of finite moment problems, J. Comp. Appl. Math. 65 (1995) 145-155, jou>

HeinigRost2011, Fast algorithms for Toeplitz and Hankel matrices, Linear Algebra Appl. 435 (2011) 1–59, gen>

PeartWoan2000a, Generating functions via Hankel and Stieltjes matrices, J. Integer Seq. Vol. 3 (2000), Article 00.2.1,  jis>

Woan2001, Hankel matrices and lattice paths, J. Integer Seq. Vol. 4 (2001), Article 01.1.2, jis>

harmonic

AskeySuslov1993, The q-harmonic oscillator and the Al-Salam and Carlitz polynomials, arXiv (9 jul 1993), aXv>

Boyadzhiev2009, Harmonic number identities via Euler’s transform, J. Integer Seq. Vol. 12 (2009), Article 09.6.1,   jis>

Boyadzhiev2012, Series with central binomial coefficients, Catalan numbers, and harmonic numbers, J. Integer Seq. Vol. 15 (2012), Article 12.1.7, jis>

Cheon G-S.El-Mikkawy2007, Generalized harmonic numbers identities and a related matrix representation, J. Korean Math. Soc. 2007 Vol. 44, No. 2, 487-498, nat>

Cheon G-S.El-Mikkawy2008, Generalized harmonic numbers with Riordan arrays, J. Number Theory Vol. 128, Issue 2, Feb 2008, 413–425, jou>

Chu2012b, Summation formulae involving harmonic numbers, Filomat 2012 Vol. 26, Issue 1, 143-152, gen>

DilKurt2011, Polynomials related to harmonic numbers and evaluation of harmonic number series II, Appl. Anal. Discrete Math. 5 (2011), 212-229, gen>

El-DesoukyGomaa2011, q-Comtet and generalized q-harmonic numbers, J. Math. Sci.Adv. Appl. Vol. 10, Number 1/2, 2011, 33-52, jou>

Feng C-J.Zhao F-Z.2009, Some results for generalized harmonic numbers, Integers 9 (2009), 605-619, gen>

Sofo2012c, Harmonic numbers of order two, Miskolc Math. Notes, Vol. 13 (2012), No. 2, 499–514, nat>

Sun Z-W.2012b, On harmonic numbers and Lucas sequences, Publ. Math. Debrecen 80 (2012), no. 1-2, 25-41, nat>

Sun Z-W.Zhao L-L.2013, Arithmetic theory of harmonic numbers (II), Colloq. Math. 130 (2013), no. 1, 67-78, gen>

ZhangWuyungaowa2013, Some identities involving generalized harmonoic polyn. and power, Int. J. Pure Appl. Math. Vol. 84, No. 1, 2013, 141-148, gen>

Hermite

AraciAcikgozBagdasaryanSen2013, The Legendre polynomials associated with Bernoulli, Euler, Hermite and Bernstein polynomials, Turkish J. Anal. Number Theory, 2013, Vol. 1, No. 1, 1-3,  nat>

BojdiAhmadi-AslAminataei2013, Operational matrices with respect to Hermite polyn. and their applications in solving linear differential equations with variable coeff., J. of Linear and Topological Algebra Vol. 02, No. 02, 2013, 91-103, jou>

Cesarano2014, A note on generalized Hermite polynomials, Int. J. Appl. Math. Informatics Vol. 8, 2014, gen>

ChaggaraKoepf2011, On linearization and connection coefficients for generalized Hermite polynomials, J. Comp. Appl. Math. Vol. 236, Issue 1, Aug 2011, 65-73,  jou>

ChatterjeaAli1991, Some formulas of L. Carlitz on Hermite polynomials, Int. J. Math. Math. Sci. Vol. 14 (1991), Issue 4, 737-740, gen>

Djordjevic1996, On some properties of generalized Hermite polynomials, Fibonacci Quart. 1996 (34,1): 2-6, fibqy>

Ghanmi2013, Operational formulae for the complex Hermite polynomials Hp,q(z, z^), arXiv (10 Jan 2013), aXv>

HabibullahShakoor2013, A generalization of Hermite polynomials, Int. Math. Forum, Vol. 8, 2013, no. 15, 701-706, gen>

HussainSingh1980, Some properties of orthogonal polynomials related to Hermite polynomials, Indian J. Pure Appl. Math. 11(8): 1018-1020, Aug 1980, nat>

IsmailMasson1994, q-Hermite polynomials, biorthogonal rational functions, and q-beta integrals, Trans. Amer. Math. Soc. Vol. 346, No. 1, (Nov 1994), 63-116, nat>

KarginKurt2013, Some relations on Hermite matrix polynomials, Math. Comput. Appl. Vol. 18, No. 3, 323-329, 2013, gen>

KimKim2012b, Extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials, Abstr. Appl. Anal. Vol. 2012 (2012), Article ID 957350, 15 p, gen>

KimKim2013b, A note on the Hermite numbers and polynomials, Math. Inequal. Appl. Vol. 16, No. 4 (2013), 1115-1122, gen>

KimKimRimLee2012, Hermite polynomials and their applications associated with Bernoulli and Euler numbers, Discrete Dyn. Nat. Soc. Vol. 2012, Article ID 974632, 13 p, gen>

Lawi2008, Hermite and Laguerre polynomials and matrix valued stochastic processes, Electron. Commun. Probab. 13 (2008), 67-84, gen>

Nagel1994, The relativistic Hermite polynomial is a Gegenbauer polynomial, J. Math. Phys. 35, 1549 (1994), jou>

Radulescu2008, Rodrigues-type formulae for Hermite and Laguerre polynomials, An. S¸t. Univ. Ovidius Constant¸a Vol. 16 (2), 2008, 109-116, nat>

SinghalJoshi1982a, On the unification of generalized Hermite and Laguerre polynomials, Indian J. Pure Appl. Math. 13(8): 904-906, August 1982, nat>

SinghalJoshi1982b, On the unification of generalized Hermite and Laguerre polyn., Revista matemática hispanoamericana Vol. 42, Nş. 1-3, 1982, 82-89, nat>

Szablowski2013, On the q-Hermite polyn. and their relationship with some other families of orthogonal polyn., Demonstratio Math. Vol. XLVI No 4 2013, gen>

Hermite big q-polynomials

FloreaniniLeTourneuxVinet1995, An algebraic interpretation of the continuous big q-Hermite polynomials, arxiv (26 Apr 1995), aXv>

Hessenberg

BenjaminShattuck2007, Recounting determinants for a class of Hessenberg matrices, Integers 7 (2007), gen>

EscribanoGiraldoSastreTorrano2011, Hessenberg matrix for sums of Hermitian positive definite matrices and weighted shifts, J. Comput. Appl. Math. Vol. 236, Issue 1, Aug 2011, 98–106, jou>

Janjic2010, Hessenberg matrices and integer sequences, J. Integer Seq. Vol. 13 (2010), Article 10.7.8, jis>

KaygisizSahin2012a, Determinant and permanent of Hessenberg matrix and Fibonacci type numbers, Gen. Math. Notes Vol. 9, No. 2, April 2012, 32-41, gen>

KaygisizSahin2012c, Generalized bivariate Lucas p-polynomials and Hessenberg matrices, J. Integer Seq. Vol. 15 (2012), Article 12.3.4, jis>

KaygisizSahin2013b, Determinants and Permanents of Hessenberg matrices and generalized Lucas polynomials, Bull. Iranian Math. Soc. Vol. 39 No. 6 (2013), 1065-1078, nat>

Horadam

Gauthier1998, Identities for a class of sums involving Horadam's generalized numbers {Wn}, Fibonacci Quart. 1998 (36,4): 295-304, fibqy>

Haukkanen2002, A note on Horadam's sequence, Fibonacci Quart. 2002 (40,4): 358-361, fibqy>

Hilton1974, On the partition of Horadam's generalized sequences into generalized Fibonacci and generalized Lucas sequences, Fibonacci Quart. 1974 (12,4): 339-344, fibqy>

HorzumKocer2009, On some properties of Horadam polynomials, Int. Math. Forum, 4, 2009, no. 25, 1243 - 1252, gen>

YazlikTaskara2012, A note on generalized k-Horadam sequence, Comput. Math. Appl. Vol. 63, Issue 1, Jan 2012, 36–41, gen>

Humbert

LamiriOuni2008, d-orthogonality of Humbert and Jacobi type polynomials, J. Math. Anal. Appl. Vol. 341, Issue 1, May 2008, 24–51, jou>

identities, inequalities

Agoh2014, Convolution identities for Bernoulli and Genocchi polynomials, Electron. J. Combin. 21 (1) (2014), gen>

AkyuzHalici2013, On some combinatorial identities involving the terms of generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat. Vol. 42 (4) (2013), 431-435, gen>

AtanassovKnottOzekiShannonSzalay2003, Inequalities among related pairs of Fibonacci numbers, Fibonacci Quart. 2003 (41,1):  20-22, fibqy>

Azarian2012a, Fibonacci identities as binomial sums, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 38, 1871-1876, gen>

Azarian2012b, Fibonacci identities as binomial sums II, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 42, 2053-2059, gen>

Azarian2012c, Identities involving Lucas or Fibonacci and Lucas numbers as binomial sums, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 45, 2221-2227, gen>

BabusciDattoliGorskaPenson2012, Generating functions for Laguerre polynomials: new identities for Lacunary Series, arXiv (13 Oct 2012), aXv>

BasorEhrhardt1999, On a class of Toeplitz + Hankel operators, New York J. Math. 5 (1999) 1-16, nat>

BasorEhrhardt2000, Some identities for determinants of structured matrices, arXiv (9 Aug 2000), aXv>

BasorWidom2000, On a Toeplitz determinant identity of Borodin and Okounkov, arXiv (9 Apr 2000), nat>

BelbachirBousbaa2014b, Combinatorial identities for the r-Lah numbers, Ars Comb. 115: 453-458 (2014), gen>

BelbachirKomatsuSzalay2014, Linear recurrences associated to rays in Pascal's triangle and combinatorial identities, Math. Slovaca 64 (2014), No. 2, 287–300, nat>

BelbachirRahmani2013, On Gessel-Kaneko’s identity for Bernoulli numbers, Appl. Anal. Discrete Math. 7 (2013), 1–10, gen>

BenjaminQuinn1999, Recounting Fibonacci and Lucas identities, College Math. J. Vol. 30, No. 5 (Nov., 1999), 359-366, gen>

BenjaminQuinnRouse2004, Fibinomial identities, Proc. of the 10th Int. Conf. on Fibonacci nbs. and their Appl. 2004, Vol. 9, 19-24, gen>

BenjaminRouse2004, Recounting binomial Fibonacci identities, Proc. of the 10th Int. Conf. on Fibonacci nbs. and their Appl. 2004, Vol. 9, 25-28, gen>

BhargavaAdigaSomashekara1993, Three-square theorem as an application of Andrew's identity, Fibonacci Quart. 1993 (31,2):  129-132, fibqy>

BibakHaghighi2009, Some trigonometric identities involving Fibonacci and Lucas numbers, J. Integer Seq. Vol. 12 (2009), Article 09.8.4, jis>

Brietzke2008, An identity of Andrews and a new method for the Riordan array proof of combinatorial identities, Discrete Math. Vol. 308, Issue 18, Sep 2008, 4246–4262, gen>

CamposCatarinoAiresVascoBorges2014, On some identities of k-Jacobsthal-Lucas numbers, Int. J. Math. Analysis, Vol. 8, 2014, no. 10, 489 - 494, gen>

CanDagli2014, Extended Bernoulli and Stirling matrices and related combinatorial identities, Linear Algebra Appl. Vol. 444, Mar 2014, 114-131 arXiv(4 Dec 2013), aXv>

CandelpergherCoppo2012, A new class of identities involving Cauchy numbers, harmonic numbers and zeta values, Ramanujan J. April 2012, Volume 27, Issue 3, 305-328, gen>

CheonEl-Mikkawy2007, Generalized harmonic numbers identities and a related matrix representation, J. Korean Math. Soc. 2007 Vol. 44, No. 2, 487-498, nat>

Chu1997b, Inverse series relations, formal power series and Blodgett-Gessel’s type binomial identities, Collect. Math. 48, 3 (1997), 265–279, gen>

ChungGrahamKnuth2010, A symmetrical Eulerian identity, J. Comb. Vol. 17, No. 1, 29–38, 2010, jou>

ChuWei2008, Legendre inversions and balanced hypergeometric series identities, Discrete Math. Vol. 308, Issue 4, 28 Feb 2008, 541–549, gen>

DaykinDresel1967, Identities for products of Fibonacci and Lucas numbers, Fibonacci Quart. 1967 (5,4):  367-369, fibqy>

Diaz-Barrero2003, Rational identities and inequalities involving Fibonacci and Lucas numbers, J. Inequalities in Pure and Applied Math, Vol. 4, Issue 5, Article 83, jou>

Farrokhi2009, An identity in the generalized Fibonacci numbers and its applications, Integers 9 (2009), 497-513, gen>

Gould2002, Generalized Bernoulli and Euler polynomial convolution identities, xxxx, xxxx>

Hansen1972, Generating identities for Fibonacci and Lucas triples, Fibonacci Quart. 1972 (10,6):  571-578, fibqy>

Hansen1978, General identities for linear Fibonacci and Lucas summations, Fibonacci Quart. 1978 (16,2):  121-127, fibqy>

Huang1997, Applications of residues to combinatorial identities, Proc. Amer. Math. Soc. 125 (1997), 1011-1017, nat>

Huangxxxx, Identities of Bernoulli numbers and polynomials, xxxx, xxxx>

IrmakAlp2013, Some identities for generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat. Vol. 42 (4) (2013), 331–338, gen>

J. Pita Ruiz V.2016, Carlitz-type and other Bernoulli identities, J. Integer Seq. Vol. 19 (2016), Article 16.1.8,

Jennings1994, On sums of reciprocals of Fibonacci and Lucas numbers, Fibonacci Quart. 1994 (32,1): 18-21,

KayllPerkins2009, Combinatorial proof of an Abel-type identity, J. Combin. Math. Combin. Comput. 2009, vol.70:  33-40,

KimKim2012e, Some identities of Frobenius-Euler polynomials arising from umbral calculus, Adv. Difference Equ. 2012, 2012: 196,

KimKimDolgyRim2013, Some identities of higher-order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus, J. Inequal. Appl. 2013, 2013: 211, KimKimDolgyRim2013, Some identities of higher-order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus, J. Inequal. Appl. 2013, 2013: 211, KimKimLee2013b, Some identities arising from Sheffer sequences for the powers of Sheffer pairs under umbral composition, Appl. Math. Sci. (Ruse) Vol. 7, 2013, no. 106, 5287-5299,

KimKimLeeDolgyRim2011, Some new identities on the Bernoulli and Euler numbers, Discrete Dyn. Nat. Soc. Vol. 2011, Article ID 856132, 11 p,

KimKimLeeRim2013, Some identities of Bernoulli, Euler and Abel polynomials arising from umbral calculus, Adv. Difference Equ. 2013, 2013: 15,

KimKimRim2014, Some identities of polynomials arising from umbral calculus, J. Comput. Anal. Appl. Jan 2014, Vol. 16, Issue 1, 293-306,

KimKimRimDolgy2013b, Some identities of Frobenius-type Eulerian polynomials arising from umbral calculus, Int. J. Math. Anal. (Ruse), Vol. 7, 2013, no. 53, 2637-2644,

KimKurtKurt2013, Some identities on the generalized q-Bernoulli, q-Euler, and q-Genocchi polynomials, Abstr. Appl. Anal. Vol. 2013, Article ID 293532, 6 p, KimKurtKurt2013, Some identities on the generalized q-Bernoulli, q-Euler, and q-Genocchi polynomials, Abstr. Appl. Anal. Vol. 2013, Article ID 293532, 6 p, KimRimDolgyLee2012, Some identities on Bernoulli and Euler polyn. arising from the orthogonality of Laguerre polyn., Adv. Difference Equ. 2012, 2012: 201, KimRimKim2012, Some identities on Bernoulli and Euler polyn. arising from orthogonality of Legendre polynomials, J. Inequal. Appl. 2012, 2012: 227, jou>

Kirillov2004, Cauchy identities for universal Schubert polynomials, J. Math. Sci. May 2004, Vol. 121, Issue 3, 2360-2370,

Koelink1995, Identities for q-ultraspherical polynomials and Jacobi functions, Proc. Amer. Math. Soc. 123 (1995), 2479-2487,

LiangWuyungaowa2012, Identities involving generalized harmonic numbers and other special combinatorial sequences, J. Integer Seq. Vol. 15 (2012), Article 12.9.6,

LiuWang W.2012, Harmonic number identities via hypergeometric series and Bell polynomials, Integral Transforms Spec. Funct. Vol. 23, Issue 1, 2012,

Mansour2004b, Rational identities and inequalities, J. of Inequalities in Pure and Applied Math. Vol. 5, Issue 3, Article 75, 2004,

Mansour2005, Generalizations of some identities involving the Fibonacci numbers, Fibonacci Quart. 2005 (43,4): 307-315,

MansourSun2009, Identities involving Narayana polynomials and Catalan numbers, Discrete Math. Vol. 309, Issue 12, Jun 2009, 4079–4088,

Mc LaughlinSury(add)2005, Addendum to: Powers of a matrix and combinatorial identities, Integers 5 (2005),

MelhamShannon1995a, Some summation identities using generalized Q-matrices, Fibonacci Quart. 1995 (33,1): 64-73,

MelhamShannon1995b, A generalization of the Catalan identity and some consequences, Fibonacci Quart. 1995 (33,1): 82-84,

Mikic2016, A Proof of a Famous Identity Concerning the Convolution of the Central Binomial Coefficients, J. Integer Seq. Vol. 19 (2016), Article 16.6.6,

NkwantaTefera2013, Curious relations and identities involving the Catalan generating function and numbers, J. of Integer Seq. Vol. 16 (2013), Article 13.9.5, jis>

J. Pita Ruiz V.2016, Carlitz-type and other Bernoulli identities, J. Integer Seq. Vol. 19 (2016), Article 16.1.8, jis>

RimJeongLee2012, Identities on the Bernoulli and Genocchi numbers and polynomials, Int J. Math. Mathematical Sciences. Vol. 2012 (2012), Article ID 184649, 9 p, gen>

Robbins1982, Some identities and divisibility properties of linear second-order recursion sequences, Fibonacci Quart. 1982 (20,1): 21-23, fibqy>

Scott1968, Continuous extensions of Fibonacci identities, Fibonacci Quart. 1968 (6,4):  245-249, fibqy>

SeibertTrojovsky2005, On some identities for the Fibonomial coefficients, Math. Slovaca, Vol. 55 (2005), No. 1, 9-19, nat>

SiarKeskin2013, Some new identities concerning generalized Fibonacci and Lucas numbers, Hacet. J. Math. Stat. Vol. 42 (3) (2013), 211-222, gen>

SinghBhadouriaSikhwal2011, Generalized identities involving common factors of Fibonacci and Lucas numbers, Int. J. Algebra Vol. 5, 2011, no. 13, 637-645, gen>

Smith2008-09, On an `uncounted' Fibonacci identity and its q-analogue, Fibonacci Quart. 2008-09 (46-47,1): 73-78, fibqy>

Sofo2012d, New classes of harmonic number identities, J. Integer Seq. Vol. 15 (2012), Article 12.7.4, jis>

SofoCerone1998a, Generalization of Euler's identity, Bull. Austral. Math. Soc. Vol. 58 (1998), 359-371, nat>

SomashekaraMurthy2014, Applications of an identity of Andrews, Arab J. Math. Sci. 20 (2) (2014), 205–212, nat>

Spieb1990, Some identities involving harmonic numbers, Math. Comp. Vol. 5, No. 192, Oct 1990, 839-863, gen>

Swamy1997a, On certain identities involving Fibonacci and Lucas numbers, Fibonacci Quart. 1997 (35,3): 230-232, fibqy>

Tingting W.Wenpeng Z.2012, Some identities involving Fibonacci, Lucas polynomials and their applications, Bull. Math. Soc. Sci. Math. Roumanie Tome 55 (103) No. 1, 2012, 95-103, nat>

Wang M.2007, An inequality and its q-analogue, J. Inequal. Pure Appl. Math. Vol. 8 (2007), Issue 2, Article 50, 6 p, jou>

Wang W.2010b, Riordan arrays and harmonic number identities, Comput. Math. Appl. Vol. 60, Issue 5, Sep 2010, 1494–1509, gen>

Wang W.Wang T.2008a, Identities via Bell matrix and Fibonacci matrix, Discrete Appl. Math. Vol. 156, Issue 14, 28 Jul 2008, 2793–2803, gen>

Wang W.Wang T.2009, Identities on Bell polynomials and Sheffer sequences, Discrete Math. Vol. 309, Issue 6, 6 Apr 2009, 1637–1648, gen>

Wloch2013, Some identities for the generalized Fibonacci numbers and the generalized Lucas numbers, Appl. Math. Comput. Vol. 219, Issue 10, Jan 2013, 5564–5568, gen>

WuSunPan2004, Some identities for Bernoulli and Euler polynomials, Fibonacci Quart. 42 (2004) (42, 4):  295–299, fibqy>

WuZhang2012, The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials, J. Inequal. Appl. 2012, 2012: 134,

WuZhang2013b, Several identities involving the Fibonacci polynomials and Lucas polynomials, J. Inequal. Appl. 2013, 2013: 205, jou>

YuanZhang2002, Some identities involving the Fibonacci polynomials, Fibonacci Quart. 2002 (40,4): 314-318, fibqy>

YuLiang1997, Identities involving partial derivatives of bivariate Fibonacci and Lucas polynomials, Fibonacci Quart. 1997 (35,1): 19-23, fibqy>

Zhang W.1997, Some identities involving the Fibonacci numbers, Fibonacci Quart. 1997 (35,3): 225-229, fibqy>

Zhang W.2004, Some identities involving the Fibonacci numbers and Lucas numbers, Fibonacci Quart. 2004 (42,2):  149-154, fibqy>

Zhang Z.1997b, Some identities involving generalized second-order integer sequences, Fibonacci Quart. 1997 (35,3): 265-268, fibqy>

Zhang Z.Liu1998b, Generalizations of some identities involving generalized second-order integer sequences, Fibonacci Quart. 1998 (36,4): 327-328, fibqy>

ZhangWuyungaowaMa2013, A class of formal operators for combinatorial identities and its application, Int. J. of Mathematical, Comput., Physical and Quantum Engineer. Vol. 7, No:3, 2013, gen>

Zhao F.Wang T.(errata)2001a, Errata for "Generalizations of some Identities Involving the Fibonacci numbers", Fibonacci Quart. 2001 (39,5): 408, fibqy>

Zhao F.Wang T.2001a, Generalizations of some identities involving the Fibonacci numbers, Fibonacci Quart. 2001 (39,2): 165-167, fibqy>

Zhao F.Wang T.2001b, Some identities for the generalized Fibonacci and Lucas functions, Fibonacci Quart. 2001 (39,5): 436-438, fibqy>

Zhao F-Z.Wang T.2003, Some identities involving the powers of the generalized Fibonacci numbers, Fibonacci Quart. 2003 (41,1): 7-12, fibqy>

incomplete numbers, generalized numbers, polynomials

ChuVicenti2003, Funzione generatrice e polinomi incompleti di Fibonacci e Lucas, Boll. Unione Mat. Ital. Serie 8, Vol. 6-B (2003), n.2, 289–308, nat>

Djordjevic2004, Generating functions of the incomplete generalized Fibonacci and generalized Lucas numbers, Fibonacci Quart. 2004 (42,2): 106-113, fibqy>

DjordjevicSrivastava2005, Incomplete Generalized Jacobsthal and Jacobsthal-Lucas Numbers, Math. Comput. Modelling, Vol. 42, Issues 9-10, Nov 2005, 1049–1056, gen>

PintérSrivastava1999, Generating functions of the incomplete Fibonacci and Lucas numbers, Rend. Circ. Mat. Palermo (2), Tomo XLVII! (1999), 591-596, nat>

Ramirez2013a, Incomplete -Fibonacci and -Lucas numbers, Chinese Journal of Mathematics Volume 2013, Article ID 107145, 7 p, nat>

Ramirez2013b, Bi-periodic incomplete Fibonacci sequences, Ann. Math. Inform. 42 (2013), 83–92, gen>

Ramirez2013c, Incomplete generalized Fibonacci and Lucas polynomials, Hacet. J. Math. Stat. Vol. 44 (2) (2015), 369–379, gen>

integer sequences

Barry2007b, Some observations on the Lah and Laguerre transforms of integer sequences, J. Integer Seq. Vol. 10 (2007), Article 07.4.6, jis>

BarryHennessy2010b, Meixner-type results for Riordan arrays and associated integer sequences, J. Integer Seq. Vol. 13 (2010), Article 10.9.4, jis>

Bedratyuk2012, A note about invariant polynomial transformations of integer sequences, J. Integer Seq. Vol. 15 (2012), Article 12.7.3, jis>

BernsteinSloane1995, Some canonical sequences of integers, Linear Algebra Appl 226-228: 57-72 (1995), gen>

Kimberling2003, Matrix transformations of Integer Sequences, J. Integer Seq. Vol. 6 (2003), Article 03.3.3,  jis>

Rudolph-Lilith2016, On the product representation of number sequences, with applications to the family of generalized Fibonacci numbers, J. Integer Seq. Vol. 19 (2016), Article 16.3.6, jis>

Zhang Z.1997b, Some identities involving generalized second-order integer sequences, Fibonacci Quart. 1997 (35,3):  265-268,  fibqy>

inverse (reciprocal) numbers, sums, polynomials

Chu1997b, Inverse series relations, formal power series and Blodgett-Gessel’s type binomial identities, Collect. Math. 48, 3 (1997), 265–279, 

Chu2012a, Reciprocal formulae for convolutions of Bernoulli and Euler polynomials, Rend. Mat. Appl. (7), Serie VII Vol. 32, Roma (2012), 17-74,

ChuHsu1993, On some classes of inverse series relations and their applications, Discrete Math. Vol. 123, Issues 1–3, Dec 1993, 3–15,  gen>

ChuMagli2007, Summation formulae on reciprocal sequences, European J. Combin. Vol. 28, Issue 3, Apr 2007, 921–930, gen>

EgorychevZima2005, Decomposition and group theoretic characterization of pairs of inverse relations of the Riordan type, Acta Appl. Math. (2005) 85:  93–109, gen>

Riordan1964, Inverse relations and combinatorial identities, Amer. Math. Monthly vol.71, No. 5 (May, 1964), 485-498, nat>

WuZhang2012, The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials, J. Inequal. Appl. 2012, 2012: 134,

Yang S-l.2013, Some inverse relations determined by Catalan matrices, Int. J. Comb. Vol. 2013 (2013), Article ID 528584, 6 p, 

YuanHeZhou2014, On the sum of reciprocal generalized Fibonacci numbers, Abstr. Appl. Anal. Vol. 2014 (2014), Article ID 402540, 4 p,

inversion techniques

Adukov1998, Generalized inversion of block Toeplitz matrices, Linear Algebra App 274:  85-124 (1998),  gen>

Adukov1999, Generalized inversion of finite rank Hankel and Toeplitz operators with rational matrix symbols, Linear Algebra App 290 (1999), 119-134,  gen>

AdukovIbryaeva2005, Generalized inversion of Toeplitz-plus-Hankel matrices, arXiv (2 Mar 2005), aXv>

AdukovIbryaeva2012, Inversion of the Toeplitz-plus-Hankel matrices via generalized inversion, Int. J. Pure Appl. Math. 79 No. 1 2012, 57-65,  gen>

Chapman2008, Lagrange inversion and Stirling number convolutions, Integers 8 (2008), gen>

Chu1994a, Inversion techniques and combinatorial identities. - A unified treatment for the 7F6–series identities, Collect. Math. 45, 1 (1994), 13–43, gen>

Chu1994b, Inversion techniques and combinatorial identities. Strange evaluations of basic hypergeometric series, Compos. Math. tome 91, no 2 (1994), 121-144, gen>

Chu1995, Inversion techniques and combinatorial identities. Jackson’s q-analogue of the Dougall-Dixon theorem and the dual formulae, Compos. Math. 95: 43-68, 1995, gen>

Chu1997b, Inverse series relations, formal power series and Blodgett-Gessel’s type binomial identities, Collect. Math. 48, 3 (1997), 265–279, 

Chu2002, Inversion techniques and combinatorial identities: balanced hypergeometric series, Rocky Mountain J. Math. Vol. 32, No. 2 (2002), 561-588, nat>

ChuWei2008, Legendre inversions and balanced hypergeometric series identities, Discrete Math. Vol. 308, Issue 4, 28 Feb 2008, 541–549, gen>

KoekoekKoekoek1999, The Jacobi inversion formula, arXiv (27 Aug 1999),  aXv>

Krattenthaler1988, Operator methods and Lagrange inversion: a unified approach to Lagrange formulas, Trans. Amer. Math. Soc. Vol. 305, No. 2, Feb 1988, 431-465, nat>

Lenart2000, Lagrange Inversion and Schur Functions, J. Algebraic Combin. 11 (2000), 69–78, jou>

LiuDingQi2012, Gould-Hsu inversion chains and their applications, J. of Math. Research with Applications, Mar 2012, Vol. 32, No. 2, 167–173,  jou>

Pan2012, Matrix decomposition of the unified generalized Stirling numbers and inversion of the generalized factorial matrices, J. Integer Seq. Vol. 15 (2012), Article 12.6.6, , jis>

Woan2007, The Lagrange inversion formula and divisibility properties, J. Integer Seq. Vol. 10 (2007), Article 07.7.8, jis>

Jacobi (see also elliptic)

AltinAktasErkus-Duman2009, On a multivariable extension for the extended Jacobi polynomials, J. Math. Anal. Appl. 353 (2009) 121–133, jou>

Askey1978, Jacobi's generating function for Jacobi polynomials, Proc. Amer. Math. Soc. Vol. 71, No. 2 (Sep. 1978), 243-246, nat>

BianePitmanYor2001, Probability laws related to the Jacobi theta and Riemann z-functions, and Brownian motion excursions, Bull. Amer. Math. Soc. (N.S.) Vol. 38, no. 4, 435-465, nat>

Bloemendal2012, Jacobi matrices, xxxx, xxxx>

Brafman1951, Generating functions of Jacobi and related polynomials, Proc. Amer. Math. Soc. (1951) xxxx, nat>

CaglieroKoornwinder2014, Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials, arXiv (15 Apr 2014), aXv>

ChandraSamantaBera2013, On bilateral generating functions of extended Jacobi polynomials, Int. J. Contemp. Math. Sci. Vol. 8, 2013, no. 20, 1001 - 1005, gen>

ChatterjeaSrivastava1993, A unified presentation of certain operational formulas for the Jacobi and related polynomials, Applied Math. and Computation, Vol. 58, Issue 1, 15 Sep 1993, 77-95, gen>

CsordasCharalambidesWaleffe2005, A new property of a class of Jacobi polynomials, Proc.  Amer. Math. Soc. Vol. 133, No. 12, 3551–3560, nat>

EliasGingold2007, On the approximation of the Jacobi polynomials, Rocky Mountain J. Math. Vol. 37, No. 1, 2007, nat>

FoataLeroux1983, Polynômes de Jacobi, interprétation combinatoire et fonction génératrice, Proc. Amer. Math. Soc. Vol. 87, No. 1 (Jan-Apr, 1983), 47-53, nat>

GriffithsSpano2011, Multiv. Jacobi and Laguerre polyn., infinite-dimens. extensions and their prob. connect. with multiv. Hahn and Meixner polynomials, Bernoulli 17 (3), 2011, 1095–1125, gen>

Hetyei2008, Delannoy numbers and a combinatorial  proof of the orthogonality of the Jacobi polynomials with natural number parameters, 23rd Clemson mini-Conference on Discrete Math. and Algorithms, Clemson, SC, Oct 2, 2008, gen>

Hetyei2009, Shifted Jacobi polynomials and Delannoy numbers, arXiv (24 Dec 2009), aXv>

KhanAkhlaq2012, A note on generating functions and summation formulas for Meixner polynomials of several variables, Demonstratio Math. Vol. XLV, No. 1, 2012, gen>

Koelink1996, On Jacobi and continuous Hahn polynomials, Proc. Amer. Math. Soc. 124 (1996), 887-898, nat>

Koornwinder1977, Yet another proof of the addition formula for Jacobi polynomials, J. Math. Anal. Appl. Vol. 61, Issue 1, 1 Nov 1977, 136–141, jou>

Koornwinder1990, Jacobi functions as limit cases of q-ultraspherical polynomials, J. Math. Anal. and Appl. Vol. 148, Issue 1 (May 1990) 44–54, jou>

Kubo2009, Generating functions of Jacobi polynomials, Commun. Stoch. Anal. Vol. 3, No. 2 (2009) 249-267, gen>

LamiriOuni2008, d-orthogonality of Humbert and Jacobi type polynomials, J. Math. Anal. Appl. Vol. 341, Issue 1, May 2008, 24–51, jou>

Lewanowicz1986, Properties of the polynomials associated with the Jacobi polynomials, Math. Comp. 47, No. 176, Oct 1986, 669-682, gen>

MadhekarThakare1982, Biorthogonal polynomials suggested by the Jacobi polynomials, Pacific J. Math. Vol. 100, No. 2 (1982), 417-424, nat>

Manocha1967, Some bilinear generating functions for Jacobi polynomials, Math. Proc. Cambridge Philos. Soc. Vol. 63, Issue 02, Apr 1967, 457-459, nat>

ManochaSharma1967, Generating functions of Jacobi polynomials, Math. Proc. Cambridge Philos. Soc. Vol. 63, Issue 02, Apr 1967, 431-433, nat>

MorenoGarcia-Caballero2011b, Non-classical orthogonality relations for continuous q-Jacobi polynomials, Taiwanese J. of Math. Vol. 15, No. 4, 1677-1690, Aug 2011, nat>

Mukherjee1996, Generating functions on extended Jacobi polynomials from Lie group view point, Publ. Mat. Vol 40 (1996), 3–13, gen>

MunotMathur1982, On a multilateral generating function for the extended Jacobi polynomials, Indian J. Pure Appl. Math. 13(5): 597-600, May 1982, nat>

Pilehrood Kh.Pilehrood T.Tauraso2012, Congruences concerning Jacobi polynomials and Apéry polynomials and Apéry-like formulae, Int. J. Number Theory, 8 (2012), no. 7, 1789–1811, gen>

Sauer2004, Jacobi polynomials in Bernstein form, Lehrstuhl füNumerische Mathematik, Justus–Liebig–Universität Gießen, nat>

Srivastava1974, Note on certain generating functions for Jacobi and Laguerre polyn.,  Publications de l'Institut Mathématique 31 (1974): 149-154, nat>

Waldron2005, On the Bernstein–Bézier form of Jacobi polyn. on a simplex, Technical Report-10/14/2005 Dept. of Math., Univ. of Auckland, New Zealand, nat>

Young1992, Apéry numbers, Jacobi sums, and special values of generalized p-adic hypergeometric functions, J. Number Theory 41, 231-255 (1992), jou>

Zayed1990, Jacobi polynomials as generalized Faber polynomials, Trans. Amer. Math. Soc. Vol. 321, No. I, Sep 1990, nat>

Jacobsthal

Cerda-Morales2012, Matrix representation of the q-Jacobsthal numbers, Proyecciones Vol. 31, No 4, Dec 2012, 345-354, nat>

Cerin2007, Sums of squares and products of Jacobsthal numbers, J. Integer Seq., Vol. 10 (2007), Article 07.2.5, jis>

CookBacon2013, Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations, Ann. Math. Inform. 41 (2013), 27–39, gen>

Dasdemir2014, A study on the Jacobsthal and Jacobsthal-Lucas numbers,

DUFED 3(1), 13-18, 2014, gen>

FreySellers2000, Jacobsthal numbers and alternating sign matrices, J. Integer Seq. Vol. 3 (2000), Article 00.2.3, jis>

GuptaPanwar2012, Common factors of generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers, Int. J. Appl. Math. Research, 1 (4) (2012) 377-382, gen>

Hoggatt, Jr.Bicknell-Johnson1978b, Convolution arrays for Jacobsthal and

Fibonacci polynomials, Fibonacci Quart. 1978 (16,5): 385-402, fibqy>

Horadam1996a, Jacobsthal representation numbers, Fibonacci Quart. 1996

(34,1): 40-54, fibqy>

Horadam1997a, Jacobsthal representation polynomials, Fibonacci Quart. 1997 (35,2): 137-148, fibqy>

Horadam1997b, Rodriques' formulas for Jacobsthal-type polynomials, Fibonacci Quart. 1997 (35,4): 361-370, fibqy>

Horadam2002a, Convolutions for Jacobsthal-type polynomials, Fibonacci methods, Science Technology RMUTT J.,

Horadam2002a, Convolutions for Jacobsthal-type polynomials, Fibonacci

Quart. 2002 (40,3): 212-222, fibqy>

HoradamFilipponi1997, Derivative sequences of Jacobsthal and Jacobsthal-Lucas polynomials, Fibonacci Quart. 1997 (35,4): 352-357, fibqy>

JhalaRathoreSisodiya2014b, Some properties of k-Jacobsthal numbers  with arithmetic Indexes, Turkish J. of Analysis and Number Theory, 2014 2 (4), 119-124, JhalaSisodiyaRathore2013, On some identities for k-Jacobsthal numbers, Int. J. Math. Anal. (Ruse), Vol. 7, 2013, no. 12, 551-556,

SrisawatSripradSthityanak2015, On the k-Jacobsthal numbers by matrix

methods, Science Technology RMUTT J.,

Swamy1999, A generalization of Jacobsthal polynomials, Fibonacci Quart. 1999 (37,2): 141-144, fibqy>

Jacobsthal-Lucas

CamposCatarinoAiresVascoBorges2014, On some identities of k-Jacobsthal-Lucas numbers, Int. J. Math. Analysis, Vol. 8, 2014, no. 10, 489-494, gen>

CatarinoVascoCamposAiresBorges2015, New families of Jacobsthal and Jacobsthal-Lucas numbers, Algebra Discrete Math. Vol. 20 (2015). Nb 1, 40-54, gen>

CookBacon2013, Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations, Ann. Math. Inform. 41 (2013), 27-39, gen>

Dasdemir2014, A study on the Jacobsthal and Jacobsthal-Lucas numbers, DUFED 3(1), 13-18, 2014, gen>

GuptaPanwar2012, Common factors of generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers, Int. J. Appl. Math. Research, 1 (4) (2012) 377-382, gen>

HoradamFilipponi1997, Derivative sequences of Jacobsthal and Jacobsthal-Lucas              polynomials, Fibonacci Quart. 1997 (35,4):  352-357, fibqy>

KökenBozkurt2008, On the Jacobsthal-Lucas numbers by matrix method, Int. J. Contemp. Math. Sci. Vol. 3, 2008, n-1633, gen>

Konhauser

KarandePatil1981, Expansion formulas for Srivastava polynomials in series of the Konhauser biorthogonal polynomials, Indian J. Pure Appl. Math. 12(9): 1124-1128, Sep 1981, nat>

SrivastavaSingh1979a, On the Konhauser polynomials Yn^m(x;k), Indian J. Pure Appl. Math. 10 (9): 1121-1126, Sep 1979, nat>

SrivastavaTasdelenSekeroglu2008, Some families of generating functions for the q-Konhauser polynomials, Taiwanese J. Math. Vol. 12, No. 3, 841-850, Jun 2008, nat>

Krawtchouk

Barry2008, A note on Krawtchouk polynomials and Riordan arrays, J. Integer Seq. Vol. 11 (2008), Article 08.2.2, jis>

DiaconisGriffiths2014, An introduction to multivariate Krawtchouk polynomials and their applications, arXiv (9 Feb 2014), aXv>

FeinsilverKocik2007, Krawtchouk polynomials and Krawtchouk matrices, arXiv (7 Feb 2007), aXv>

KyriakoussisVamvakari2007, Asymptotic behaviour of a q-binomial type distribution based on q-Krawtchouk orthogonal polynomials, J. Comput. Anal. Appl. Vol. 8, No. 1, 2007, jou>

Shibukawa2014, Multivariate Meixner, Charlier and Krawtchouk polynomials, arXiv (29 Apr 2014), aXv>

lacunary series

AgohDilcher2007, Convolution identities and lacunary recurrences for Bernoulli numbers, J. Number Theory 124, Issue 1, May 2007, 105–122, jou>

AlloucheMendčs-France2013, Lacunary formal power series and the Stern-Brocot sequence, Acta Arith. Vol. 159, No. 1, (2013), 47-61, aXv>

BabusciDattoliGorskaPenson2012, Generating functions for Laguerre polynomials: new identities for lacunary series, arXiv (13 Oct 2012), aXv>

Dilcher2007, Congruences for a class of alternating lacunary sums of binomial coefficients, J. Integer Seq. Vol. 10 (2007), Article 07.10.1, jis>

Howard2004, A general lacunary recurrence formula, Proc. 10th Int. Conf. on Fibonacci numbers and their Appl. 2004, Vol. 9, 121-135, gen>

Lehmer1935, Lacunary recurrence formulas for the numbers of Bernoulli and Euler, Ann. of Math. (2), Vol. 36, No. 3, (Jul 1935), 637-649, nat>

Lengyel2007, Asymptotics for lacunary sums of binomial coefficients and a card problem with ranks, J. Integer Seq. Vol. 10 (2007), Article 07.7.2, jis>

Mendčs-France vanderPoortenShallit1998, On lacunary formal power series and their continued fraction expansion, To Andrzej Schinzel on his 60th birthday, gen>

Ramirez2013b, Bi-periodic incomplete Fibonacci sequences, Ann. Math. Inform. 42 (2013), 83–92, gen>

Young2003a, On lacunary recurrences, Fibonacci Quart. 2003 (41,1):  41-47, fibqy>

Lagrange

DattoliLorenzuttaSacchetti2001, Multivariable Lagrange expansion and generalization of Carlitz–Srivastava mixed generating functions, J. Math. Anal. Appl. Vol. 257, Issue 2, May 2001, 308–320, jou>

DattoliRicciCesarano2003, The Lagrange polynomials, the associated generalizations, and the umbral calculus, Integral Transforms Spec. Funct. Vol. 14, Issue 2, 2003, gen>

Laguerre

AlamChongdar2007, On generating functions of modified Laguerre polynomials, Rev. Real Academia de Ciencias, Zaragoza 62: 91–98, (2007), nat>

Al-Salam1984, Some operational formulas for the g-Laguerre polynomials, Fibonacci Quart. 1984 (22,2): 166-170, fibqy>

BojdiAhmadi-Asl2014, The generalized Laguerre matrix method for solving linear differential-difference equat. with variable coefficients, Appl. Appl. Math. Vol. 9, Issue 1 (Jun 2014), 272-294, gen272-294, gen>

Carlitz1968c, Some generating functions for Laguerre polynomials, Duke Math. J. Vol. 35, Number 4 (1968), 825-827, gen>

Chatterjea1963d, A generalization of Laguerre polynomials, Collect. Math. 1963, Vol.15,3: 285-292, gen>

Chatterjea1964, On a generalization of Laguerre polynomials, Rend. Semin. Mat. Univ. Padova, 1964, Vol. 34, 180-190, nat>

Chatterjea1968, A note on generalized Laguerre polynomials, Publ. Inst. Math. (Beograd) (N.S.), 8(22), 1968, 89-92, nat>

ChenIsmailMuttalib1994, Asymptotics of basic Bessel functions and q-Laguerre polynomials, J. Comput. Appl. Math. Vol. 54, Issue 3, Oct 1994, 263–272, jou>

CiccoliKoelinkKoornwinder1998, q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations, arXiv (6 May 1998), aXv>

Djordjevic2001b, On the generalized Laguerre polynomials, Fibonacci Quart. 2001 (39,5):  403-407, fibqy>

Ernst2002, Some results for q-Laguerre polyn., U.U.D.M. Report 2002:20, gen>

GhressiKhérijiTounsi2011, An introduction to the q-Laguerre-Hahn orth. q-polyn., SIGMA Symmetry Integrability Geom. Methods Appl. 7 (2011), 092, 20 p, gen>

GillisJedwabiZeilberger1988, A combinatorial interpretation of the integral of the product of Legendre polynomials , Siam J. Math. Anal. Vol. 19, No. 6, Nov. 1988, gen>

GriffithsSpano2011, Multiv. Jacobi and Laguerre polyn., infinite-dimens. extensions and their prob. connect. with multiv. Hahn and Meixner polynomials, Bernoulli 17 (3), 2011, 1095–1125, gen>

Groenevelt2003b, Laguerre functions and representations of su(1: 1), Indag.Math. (N.S.), Vol. 14, Issues 3–4, Dec 2003, 329–352, gen>

Hajir2009, Algebraic properties of a family of generalized Laguerre polynomials, Canad. J. Math. Vol. 61 (3), 2009, 583–603, nat>

KasraouiStantonZeng2011, The combinatorics of Al-Salam-Chihara q-Laguerre polynomials, Advances in Applied Math. Vol. 47, Issue 2, Aug 2011, 216-239, gen>

KhanHabibullah2012, Extended Laguerre polynomials, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 22, 1089–1094, gen>

KimKim2012b, Extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials, Abstr. Appl. Anal. Vol. 2012 (2012), Article ID 957350, 15 p, gen>

KimKimDolgy2012, Some identities on Laguerre polyn. in connection with Bernoulli and Euler numbers, Discrete Dyn. Nat. Soc. Vol. 2012, Article ID 619197, 10 p, gen>

KimRimDolgyLee2012, Some identities on Bernoulli and Euler polynomials arising from the orthogonality of Laguerre polynomials, Adv. Difference Equ. 2012, 2012: 201, gen>

Koekoek1990, Generalizations of Laguerre polynomials, J. Math. Anal. Appl. Vol. 153, Issue 2, Dec 1990, 576–590, jou>

KoekoekMeijer1993, A generalization of Laguerre polynomials, SIAM J. Math. Anal. 24-3 (1993), 768-782, gen>

Konhauser1967, Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. Vol. 21, No. 2, 1967, nat>

Lawi2008, Hermite and Laguerre polynomials and matrix valued stochastic processes, Electron. Commun. Probab. 13 (2008), 67–84, gen>

Mohanty1976, Interesting properties of Laguerre polynomials, Fibonacci Quart. 1976 (14,1): 42, fibqy>

MorenoGarcia-Caballero2011a, q-Sobolev orthogonality of the q-Laguerre polynomials Ln^(-N) ( ; q)n =0^ for positive integers N, J. Korean Math. Soc. 48 (2011), No. 5, 913-926, nat>

pahio2013, Generating function of Laguerre polynomials, xxxx, xxxx>

PérezPinar1996, On Sobolev orthogonality for the generalized Laguerre polynomials, J. Approx. Theory Vol. 86, Issue 3, Sep 1996, 278–285, jou>

Radulescu2008, Rodrigues-type formulae for Hermite and Laguerre polynomials, An. S¸t. Univ. Ovidius Constant¸a Vol. 16 (2), 2008, 109–116, nat>

Sanchez-MorenoManzanoDehesa2010, Direct spreading measures of Laguerre polynomials, J. Comput. Appl. Math. Vol. 235, Issue 5, Jan 2011, 1129–1140, jou>

Schoutens2001, An application in stochastics of the Laguerre-type polynomials, J. Comp. Appl. Math. Vol. 133, Issues 1–2, 1 Aug 2001, 593–600, jou>

Shen2000, Orthogonal polynomials on the unit circle associated with the Laguerre polynomials, Proc. Amer. Math. Soc. (2000) 129, No. 3, 873–879, nat>

ShuklaMeher2010, Generating functions for Laguerre type polynomials of two variables Ln^(a-n)(x,y) by using group theoretic method, Int. J. Math. Anal. (Ruse), Vol. 4, 2010, no. 48, 2357-2366, gen>

SimionStanton1993, Specializations of generalized Laguerre polynomials, SIAM J. Math. Anal. 25(2), 712–719. 8 p, aXv>

SinghalJoshi1982a, On the unification of generalized Hermite and Laguerre polynomials, Indian J. Pure Appl. Math. 13(8): 904-906, August 1982, nat>

SinghalJoshi1982b, On the unification of generalized Hermite and Laguerre polyn., Revista matemática hispanoamericana Vol. 42, Nş. 1-3, 1982, 82-89, nat>

SinghYadav2007, On a general class of q-polynomials suggested by basic Laguerre polynomials, Bull. Pure Appl. Math. 01(1) (2007), 94-102, nat>

Weiss1962, Laguerre expansions for successive generations of a Renewal Process, J. Research National Bureau of Standards-B. Math. and Math. Physics, Vol. 66B, No.4, Oct- Dec 1962, jou>

Zeng J.1995, The q-Stirling numbers, continued fractions and the q-Charlier and q-Laguerre polyn., J. Comp. Appl. Math. Vol. 57, Issue 3, Feb 1995, 413–424, jou>

Laguerre little q-polynomials

Ben CheikhLamiriOuni2011, d-orthogonality of llttle q-Laguerre type polynomials, J. Comp. Appl. Math Vol. 236, Issue 1, 1 Aug 2011, 74–84, jou>

MorenoGarcia-Caballero2009, Non-standard orthogonality for the Little q-Laguerre polynomials, Applied Math. Letters Vol. 22, Issue 11, Nov 2009, 1745–1749, gen>

Lah

BelbachirBousbaa2014a, Associated Lah numbers and r-Stirling numbers, arXiv (12 May 2014), aXv>

BelbachirBousbaa2014b, Combinatorial identities for the r-Lah numbers, Ars Comb. 115: 453-458 (2014), gen>

Della Riccia2004, Inversions relating Stirling, Tanh, Lah numbers and an application to Mathematical Statistics, arXiv (31May 2004), aXv>

Della Riccia2006, Converting between generalized Bell, Lah, Stirling, and Tanh numbers, J. Integer Seq. Vol. 9 (2006), Article 06.3.5, jis>

LindsayMansourShattuck2011, A new combinatorial interpretation of a q-analogue of the Lah numbers, J. Comb. Vol. 2 (2011), No. 2, 245-264, jou>

NyulRacz2014, The r-Lah numbers, Discrete Math. Vol. 338, Issue 10, Oct. 2015, 1660–1666, gen>

Tauber1965, On generalized Lah-numbers, Proc. Edinb. Math. Soc. (2), (1965) 14, 229-232, nat>

Tauber1968a, Lah numbers for Fibonacci and Lucas polynomials, Fibonacci Quart. 1968 (6,5): 93-99, fibqy>

Tauber1968b, Lah numbers for r-polynomials, Fibonacci Quart. 1968 (6,5): 100-107, fibqy>

Wagner1996, Generalized Stirling and Lah numbers, Discrete Math. Vol. 160, Issues 1–3, 15 Nov 1996, 199–218, gen>

lattice

Church Jr.1974, Lattice paths and Fibonacci and Lucas numbers, Fibonacci Quart. 1974 (12,4): 336-338, fibqy>

Dziemianczuk2013, Generalizing Delannoy numbers via counting weighted lattice paths, Integers 13 (2013), 1-33, gen>

FelsnerHeldt2015, Lattice path enumeration and Toeplitz matrices, J. Integer Seq. Vol. 18 (2015), Article 15.1.3, jis>

Hennessy2011, A study of Riordan arrays with applications to continued fractions, orthogonal polynomials and lattice paths, Thesis-Waterford Institute of Technology (Oct 2011), gen>

Lehner2003, Cumulants, lattice paths, and orthogonal polynomials, Discrete Math. Vol. 270, Issues 1–3, Aug 2003, 177–191, gen>

Nkwanta2003, A Riordan matrix approach to unifying a selected class of combinatorial arrays, Congr. Numer. 160 (2003), 33-45, gen>

Nkwanta2008, Lattice Paths, Riordan Matrices and RNA Numbers, Congr. Numer. 01/2008, gen>

Nkwanta2009, Lattice path and RNA secondary structure predictions, Fifteenth Conf. for Afri. Amer. Researchers in the Math. Sci-Rice University, June 23-26, 2009, gen>

Nkwanta2010, Riordan matrices and higher-dimensional lattice walks, J. of Statist. Plann. Inference Vol. 140, Issue 8, Aug 2010, 2321–2334, jou>

NkwantaShapiro2005, Pell walks and Riordan matrices, Fibonacci Quart. 2005 (43,2): 170-180, fibqy>

Stanley1975, The Fibonacci lattice, Fibonacci Quart. 1975 (13,3): 215-232, fibqy>

SulankeXin2006, Hankel determinants for some common lattice paths, Formal Power Series and Algebraic Combinatorics-San Diego, California 2006, gen>

Woan2001, Hankel matrices and lattice paths, J. Integer Seq. Vol. 4 (2001), Article 01.1.2, jis>

Zaremba1970, A remarkable lattice generated by Fibonacci numbers, Fibonacci Quart. 1970 (8,2): 185-198, fibqy>

Laurent

Barry2013f, Laurent biorth. polyn. and Riordan arrays, arXiv (10 Nov 2013), ErmanSmithVarilly-Alvarado2011, Laurent polynomials and Eulerian numbers, J. Combin. Theory Ser. A, Vol. 118, Issue 2, Feb 2011, 396–402, aXv>

He2011a, Riordan arrays associated with Laurent series and generalized Sheffer-type groups, Linear Algebra Appl. Vol. 435, Issue 6, Sep. 2011, 1241–1256, gen>

LDU decomposition, Cholesky factorization

BarryHennessy2012b, Riordan arrays and the LDU decomposition of symmetric Toeplitz plus Hankel matrices, Linear Algebra Appl. Vol. 437, Issue 6, Sep 2012, 1380–1393, gen>

CahillD'ErricoSpence2003, Complex factorization of the Fibonacci and Lucas numbers, Fibonacci Quart. 2003 (vol.41,1): 13-19, fibqy>

ChuiWardSmith1982, Cholesky factorization of positive definite bi-infinite matrices, Numer. Funct. Anal. Optim. Vol. 5, Issue 1, 1982, 1-20, gen>

HoradamFilipponi1991, Cholesky algorithm matrices of Fibonacci type and properties of generalized sequences, Fibonacci Quart. 1991 (29,2): 164-173, fibqy>

KoornwinderOnn2006, LU factorizations, q = 0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials, Ramanujan J. Vol. 13, Issue 1-3, (Jun 2007), 365-387, aXv>

LeeKimLee2002, Factorizations and eignvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart. 2002 (40,3): 203-211, fibqy>

Oruç2007, LU factorization of the Vandermonde matrix and its applications, Applied Math. Letters Vol. 20, Issue 9, Sep 2007, 982–987, gen>

Stanica2005, Cholesky factorizations of matrices associated with r-order recurrent sequences, Integers 5(2) (2005), gen>

Strang2013, Banded matrices with banded inverses and A=LPU, 5th Int. Congress of Chinese Mathematicians: ICCM2010, gen>

van der MeeRodrighezSeatzu1998, Block Cholesky factorization of infinite matrices and orthonormalization of vectors of functions, Lect. Notes Pure Appl. Math. 202, 423-456-Computational mathematics, gen>

Yang S-l.2005, On the LU factorization of the Vandermonde matrix, Discrete Applied Math. 146 (2005) 102–105, gen>

Legendre

AraciAcikgozBagdasaryanSen2013, The Legendre polynomials associated with Bernoulli, Euler, Hermite and Bernstein polynomials, Turkish J. Anal. Number Theory, 2013, Vol. 1, No. 1, 1-3, nat>

ChuWei2008, Legendre inversions and balanced hypergeometric series identities, Discrete Math. Vol. 308, Issue 4, 28 Feb 2008, 541–549, gen>

GarrettKillpatrick2014, Generalized Legendre-Stirling numbers, Open J. Discrete Math. 2014, 4, 109-114, gen>

GawronskiLittlejohnNeuschel2014, On the asymptotic normality of the Legendre-Stirling numbers of the second kind, arXiv (3 aug 2014), aXv>

Haggard1988, Some further results on Legendre numbers, Int. J. Math. Math. Sci. Vol. 11 (1988), Issue 3, 619-623, gen>

Hetyei2006b, Central Delannoy numbers, Legendre polynomials, and a balanced join operation preserving the Cohen-Macaulay property, Formal Power Series and Algebraic Combinatorics-San Diego, California 2006, gen>

JinDickinson2000, Apéry sequences and Legendre transforms, J. Austral. Math. Soc. (Series A) 68 (2000), 349-356, nat>

KimRimKim2012, Some identities on Bernoulli and Euler polynomials arising from orthogonality of Legendre polynomials, J. Inequal. Appl. 2012, 2012: 227, jou>

OberleScottGilbertHatcherAddis1993, Mellin transforms of a generalization of Legendre polynomials, J. Comp. Appl. Math. 45 (1993), 367-369, jou>

Schmidt1995, Legendre transforms and Apéry's sequences, J. Austral. Math. Soc. (Series A) 58 (1995), 358-375, nat>

SrivastavaSinghSingh1980, Bilateral generating functions for a new class of generalized Legendre polynomials, Int. J. Math. Math. Sci. Vol. 3, No. 2 (1980), 305-310, gen>

Strehl1992, Recurrences and Legendre Transform, Sém. Lothar. Combin. B29b (1992), 22 p. 29 Thurnau, Sep 1992, gen>

WanZudilin2011, Generating functions of Legendre polynomials: A tribure to Fred Brafman, xxxx, gen>

Lehmer

Filipponi1997b, Summation formulas for special Lehmer numbers, Fibonacci Quart. 1997 (35,3): 252-257, fibqy>

KilicStanica2010, The Lehmer matrix and its recursive analogue, J. Combinat. Math. Combinat.Comput. 74 (2010), 193-205, jou>

LucaPorubsky2003, The multiplicative group generated by the Lehmer numbers, Fibonacci Quart. 2003 (vol.41,2): 122-132, fibqy>

ShannonMelham1993, Carlitz generalizations of Lucas and Lehmer sequences, Fibonacci Quart. 1993 (31,2): 105-111, fibqy>

Lehner

Lengyel

BarskyBézivin2014, p-adic properties of Lengyel’s numbers, J. Integer Seq. Vol. 17 (2014), Article 14.7.3, jis>

L-functions

Bouganis2014, On Special L-Values attached to Siegel Modular Forms, Iwasawa theory 2012 : state of the art and recent advance, p. 135-176. Contrib. in mathematical and computational sci. (7), gen>

Chida2015, Indivisibility of central values of L-functions for modular forms, Proc. of the AMS Vol. 143, Number 7, Jul 2015, P 2829–2840, nat>

Dabrowski1994, p-adic L-functions of Hilbert modular forms, Annales de l’institut Fourier, tome 44, no 4 (1994), p 1025-1041, gen>

KimShahidi1999, Symmetric cube L-functions for GL2 are entire, Annals of Math. 150 (1999), 645–662, gen>

Kozima2002, Standard L-functions attached to vector valued Siegel modular forms, Osaka J. Math. 39 (2002), 245–258, nat>

Liu S-C.Masri2014, Nonvanishing of Rankin–Selberg L-functions for Hilbert modular forms, R. Ramanujan J (2014) 34: 227, gen>

Panchishkin2007, L-functions of Siegel modular forms, their families and lifting conjectures, Modulformen, Oct 29-Nov 2 2007, (Oberwolfach, Germany), gen>

Perelli2004, A survey of the Selberg class of L-functions, part II, R i v . M a t . U n i v . P a r m a ( 7 ) 3 * ( 2 0 0 4 ) , 8 3-1 1, nat>

Perelli2005, A survey of the Selberg class of L-functions, Part I, Milan J. of Math. Oct 2005, Vol. 73, Issue 1, p 19–52, nat>

Saha2014, Siegel modular forms of degree 2: Fourier coefficients, L-functions, and functoriality (a survey), xxxx, gen>

Saito1991, A generalization of Gauss sums and its applications to Siegel modular forms and L-functions associated with the vector space of quadratic forms, Journal für die reine und angewandte Mathematik (Crelles Journal). Vol. 1991, Issue 416, P 9–142, gen>

White2012, The base change L-function for modular forms and beyond endoscopy, J. Number Theory, Vol. 140, Jul 2014, P 13-37, gen>

Zhang S-W2002, Elliptic curves, L-functions, and CM-points, xxxx, gen>

Zhang S-W2002, Elliptic curves, L-functions, and CM-points, xxxx, gen>

linear algebra of certain matrices

BrawerPirovino1992, The Linear Algebra of the Pascal matrix, Linear Algebra Appl. Vol. 174, Sep 1992, 13–23, gen>

 KiliçTasci2005, The linear algebra of the Pell matrix, Bol. Soc. Mat. Mexicana (3) Vol. 11, 2005, nat>

Zhizheng Z.1997, The linear algebra of the generalized Pascal matrix, Linear Algebra Appl. Vol. 250, Jan 1997, 51–60, gen>

Lucas

AkyuzHalici2013, On some combinatorial identities involving the terms of generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat. Vol. 42 (4) (2013), 431-435, gen>

AndersonBenjaminRouse2005, Combinatorial proofs of Fermat's, Lucas's, and Wilson's theorems, Amer. Math. Monthly, Vol. 112, No. 3,  266-268, Mar 2005, nat>

André-Jeannin1991, A note on the irrationality of certain Lucas infinite series, Fibonacci Quart. 1991 (29,2): 132-135, fibqy>

André-Jeannin1994a, On a conjecture of Piero Filipponi, Fibonacci Quart. 1994 (32,1): 11-13, fibqy>

Antoniadis1985, Fibonacci and Lucas numbers of the form 3z^2 + 1, Fibonacci Quart. 1985 (23,4): 300-307, fibqy>

Azarian2012c, Identities involving Lucas or Fibonacci and Lucas numbers as binomial sums, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 45, 2221-2227, gen>

Ballot2014, On a congruence of Kimball and Webb involving Lucas sequences, J. Integer Seq. Vol. 17 (2014), Article 14.1.3, jis>

BelbachirBencherif2007, Sums of products of generalized Fibonacci and Lucas numbers, arXiv (17 Aug 2007), aXv>

BelbachirBencherif2008, On some properties of bivariate Fibonacci and Lucas polynomials, J. Integer Seq. Vol. 11 (2008), Article 08.2.6, jis>

BelbachirBenmezai2012, Expansion of Fibonacci and Lucas polynomials: An answer to Prodinger’s question, J. Integer Seq. Vol. 15 (2012), Article 12.7.6, jis>

Benjamin2010, The Lucas triangle recounted, Congr. Numer. Proc. 12-th Conf. on

Fib. nbs. and their Appl. Vol. 200 (2010), 237-256, gen>

Benoumhani2003, A sequence of binomial coefficients related to Lucas and Fibonacci numbers, J. Integer Seq. Vol. 6 (2003), Article 03.2.1, jis>

Bilcigi2014, New generalizations of Fibonacci and Lucas sequences, Appl. Math.     Sci. Vol. 8, 2014, no. 29, 1429-1437, gen>

BolatIpeKöse2012, On the sequence related to Lucas numbers and its properties, Math. Ćterna Vol. 2, 2012, no. 1, 63-75, gen>

Byrd1975b, Relations between Euler and Lucas numbers, Fibonacci Quart. 1975 (13,2): 111-114, fibqy>

CahillD'ErricoSpence2003, Complex factorization of the Fibonacci and Lucas numbers, Fibonacci Quart. 2003 (vol.41,1): 13-19, arXiv>

Cerda-Morales2013, On generalized Fibonacci and Lucas numbers by matrix methods, Hacet. J. Math. Stat. Vol. 42 (2) (2013), 173-179, gen>

Cerin2009, Sums of products of generalized Fibonacci and Lucas numbers,         

Demonstratio Math. Vol. XLII No 2 2009, gen>

CheonKimShapiro2009, A generalization of Lucas polynomial sequence, Discrete Appl. Math. Vol. 157, Issue 5, Mar 2009, 920–927, gen>

Falcon2012, On the Lucas triangle and its relashionship with the k-Lucas numbers, J. Math. Comput. Sci. 2 (2012), No. 3, 425-434, jou>

Feinberg1967, A Lucas triangle, Fibonacci Quart. 1967 (5,5): 486-490, fibqy>

Ferns1969, Products of Fibonacci and Lucas numbers, Fibonacci Quart. 1969 (7,1): 1-12, fibqy>

Fielder1967a, Certain Lucas-like sequences and their generation by partitions of numbers, Fibonacci Quart. 1967 (5,4): 319-324, fibqy>

FilipponiHoradam1993a, Second derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quart. 1993 (31,3): 194-204, fibqy>

FilipponiHoradam1993b(addendum), Addendum to "Second derivative sequences of Fibonacci and Lucas polynomials", Fibonacci Quart. 1993 (31,3): 194-204, fibqy>

GodaseDhakne2014, On the properties of k-Fibonacci and k-Lucas numbers, Int. J. Adv. Appl. Math. and Mech. 2 (1)  (2014), 100 - 106, gen>

Hansen1972, Generating identities for Fibonacci and Lucas triples, Fibonacci Quart. 1972 (10,6): 571-578, fibqy>

HeZhang W.2010, Sum relations for Lucas sequences, J. Integer Seq. Vol. 13 (2010), Article 10.4.6, jis>

Hilton1974, On the partition of Horadam's generalized sequences into generalized Fibonacci and generalized Lucas sequences, Fibonacci Quart. 1974 (12,4): 339-344, fibqy>

HiltonPedersenVrancken1995, On certain arithmetic properties of Fibonacci and Lucas numbers, Fibonacci Quart. 1995 (33,3): 211-217, fibqy>

Hu2002, On Lucas v-triangles, Fibonacci Quart. 2002 (40,4): 290-294, fibqy>

HuSun Z-W.2001, An extension of Lucas' theorem, Proc. Amer. Math. Soc. Vol. 129, No. 12, 3471-3478, nat>

IrmakAlp2013, Some identities for generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat. Vol. 42 (4) (2013), 331–338, gen>

Ismail2008-09, One parameter generalizations of the Fibonacci and Lucas numbers, Fibonacci Quart. 2008/09 (46/47,2): 167-179   arXiv (29 Jun 2006), aXv>

J. Pita Ruiz V.2013, Some number arrays related to Pascal and Lucas triangles, J. Integer Seq. Vol. 16 (2013), Article 13.5.7, jis>

Jarden1967, A new important formula for Lucas numbers, Fibonacci Quart. 1967 (5,4): 346, fibqy>

Jennings1994, On sums of reciprocals of Fibonacci and Lucas numbers, Fibonacci Quart.  1994 (32,1): 18-21, fibqy>

JiaLiuWang2007, q-analogs of generalized Fibonacci and Lucas polynomials, Fibonacci Quart. 2007 (45,1): 26-34, fibqy>

KappraffAdamson2004, Generalized Binet formulas, Lucas polynomials, and cyclic constants, Forma 19, 355–366, 2004, gen>

KaygisizSahin2012b, New generalizations of Lucas numbers, Gen. Math. Notes Vol. 10, No. 1, May 2012, 63-77, gen>

KaygisizSahin2012c, Generalized bivariate Lucas p-polynomials and Hessenberg matrices, J. Integer Seq. Vol. 15 (2012), Article 12.3.4, jis>

KaygisizSahin2013b, Determinants and Permanents of Hessenberg matrices  and generalized Lucas polynomials, Bull. Iranian Math. Soc. Vol. 39 No. 6 (2013), 1065-1078, nat>

Koshy2011, Fibonacci, Lucas, and Pell numbers, and Pascal’s triangle, Mathematical Spectrum 2010/2011, Vol. 43 Issue 3, 125, gen>

LeeAsci2012, Some properties of the (p,q)-Fibonacci and (p,q)-Lucas polynomials, J. Appl. Math. Vol. 2012 (2012), Article ID 264842, 18 p, jou>

Lengyel1995, The order of the Fibonacci and Lucas numbers, Fibonacci Quart. 1995 (33,3): 234-239, fibqy>

Luca2000, Equations involving arithmetic functions of Fibonacci and Lucas numbers, Fibonacci Quart. 2000 (38,1): 49-55, fibqy>

LuJang2013, The sum and product of Fibonacci numbs. and Lucas numbs., Pell numbs. and Pell-Lucas numbs. representation by matrix method, WSEAS Trans. on Math., Issue 4, Vol. 12, Apr 2013, gen>

Mahajan2014, The Binet forms for the Fibonacci and Lucas numbers, Int. J. of Math. Trends and Technology Vol.10, No. 1, Jun 2014, gen>

McDaniel1994a, On the greatest integer function and Lucas sequences, Fibonacci Quart. 1994 (32,4): 297-300, fibqy>

McDaniel1994b, The irrationality of certain series whose terms are reciprocals of Lucas sequence terms, Fibonacci Quart. 1994 (32,4): 346-351, fibqy>

McDaniel2001, On the factorization of Lucas numbers, Fibonacci Quart., 2001 (39,3): 206-210, fibqy>

Melham2000, Sums of certain products of Fibonacci and Lucas numbers-Part II, Fibonacci Quart. 2000 (38,1): 3-7, fibqy>

MollVignat2014, Generalized Bernoulli numbers and a formula of Lucas, arXiv (12 Fev 2014), aXv>

Muskat1993, Generalized Fibonacci and Lucas sequences and rootfinding methods, Math. Comp. 61 (1993), 365-372, gen>

NalliHaukkanen2009, On generalized Fibonacci and Lucas polynomials, Chaos, Solitons and Fractals Vol. 42, Issue 5, Dec 2009, 3179–3186, gen>

NalliZhang2010, On generalized Lucas polynomials and Euler numbers, Miskolc Mathematical Notes Vol. 11 (2010), No. 2, 163–167, nat>

ÖcalTugluAltinisik2006, On the representation of k-generalized Fibonacci and Lucas numbers, Applied Math. Comp. Vol. 170, Issue 1, 584-596 (1 Nov 2005), gen>

Ozgur2002, Generalizations of Fibonacci and Lucas sequences, Note di Matematica 21, n. 1, 2002, 113–125, gen>

Pandey2013, On some magnified Fibonacci numbers modulo a Lucas number, J. Integer Seq. Vol. 16 (2013), Article 13.1.7, jis>

Pethe1985, On Lucas fundamental functions and Chebychev polynomial sequences, Fibonacci Quart. 1985 (23,1):  57-65, fibqy>

Popov1985, A note on the sums of Fibonacci and Lucas polynomials, Fibonacci Quart. 1985 (23,3): 238-239, fibqy>

Prodinger2009, On the expansion of Fibonacci and Lucas polynomials, J. Integer Seq. Vol. 12 (2009), Article 09.1.6, jis>

RandicMoralesAraujo2008, Higher-order Lucas numbers, Divulg. Mat. Vol. 16, No. 2, (2008), 275–283, gen>

Robbins2005, The Lucas triangle revisited, Fibonacci Quart. 2005 (43,2): 142-148, fibqy>

SeibertTrojovsky2007, On multiple sums of products of Lucas numbers, J. Integer Seq. Vol. 10 (2007), Article 07.4.5, jis>

Shannon2010, Another generalization of the Fibonacci and Lucas numbers, Notes Number Theory Discrete Math.16 (2010), 3, 11-17, gen>

ShannonMelham1993, Carlitz generalizations of Lucas and Lehmer sequences, Fibonacci Quart. 1993 (31,2): 105-111, fibqy>

SinghSikhwalPanwar2009, Generalized determinantal identities involving Lucas polynomials, Appl. Mathematical Sci. Vol. 3, 2009, no. 8, 377-388, gen>

StakhovRozin2006, Theory of Binet formulas for Fibonacci and Lucas p-numbers, Chaos, Solitons and Fractals, Vol. 27, Issue 5, Mar 2006, 1162–1177, gen>

StanimirovicNikolovStanimirovic2008, A generalization of Fibonacci and Lucas matrices, Discrete Appl. Math. Vol. 156, Issue 14, Jul 2008, 2606–2619, gen>

Steiner1978, On N-th powers in the Lucas and Fibonacci series, Fibonacci Quart. 1978  (vol.16,5): 451-458, fibqy>

Sun Z-W.2010b, Binomial coefficients, Catalan numbers and Lucas quotients, Sci. China Math. 53 (2010), no. 9, 2473–2488, nat>

Sun Z-W.2012b, On harmonic numbers and Lucas sequences, Publ. Math. Debrecen 80 (2012), no. 1-2, 25–41, nat>

Tauber1968a, Lah numbers for Fibonacci and Lucas polynomials, Fibonacci Quart. 1968 (6,5): 93-99, fibqy>

Tauraso2016, Some congruences for central binomial sums involving Fibonacci and Lucas numbers, J. Integer Seq. Vol. 19 (2016), Article 16.5.4, jis>

Tingting W.Wenpeng Z.2012, Some identities involving Fibonacci, Lucas polynomials and their applications, Bull. Math. Soc. Sci. Math. Roumanie Tome 55 (103) No. 1, 2012, 95-103, nat>

Velasco2012, A note on Fibonacci and Lucas and Bernoulli and Euler polynomials,     J. Integer Seq. Vol. 15 (2012), Article 12.2.7, jis>

Velasco2013, Some number arrays related to Pascal and Lucas triangles, J.     Integer  Seq. Vol. 16 (2013), Article 13.5.7, jis>

Wang J.1995, On the k^th derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quart. 1995 (33,2): 174-178, fibqy>

Wang Q.2010, On generalized Lucas sequences, 20th anniv. conf. of IPM, May 15-21, 2009- Comb. and Graphs-Contemp. Math. 531 (2010), 127-141, gen>

Witula2013, Binomials transformation formulae of scaled Lucas numbers, Demonstratio Math. Vol. XLVI, No 1, 2013, 15-27, gen>

Wloch2013, Some identities for the generalized Fibonacci numbers and the generalized Lucas numbers, Appl. Math. Comput. Vol. 219, Issue 10, Jan 2013, 5564–5568, gen>

YeZhang Z.2007, Relations between the reciprocal sum and the alternating sum for generalized Lucas numbers, Acta Math. Univ. Comenianae Vol. LXXVI, 2(2007), 215–222, nat>

Young1995, Quadratic reciprocity via Lucas sequences, Fibonacci Quart. 1995 (33,1): 78-81, fibqy>

Zhang W.2004, Some identities involving the Fibonacci numbers and Lucas numbers, Fibonacci Quart. 2004 (42,2): 149-154, fibqy>

Zhao F.2001, Summation of certain reciprocal series related to the generalized Fibonacci and Lucas numbers, Fibonacci Quart. 2001 (39,5): 392-397, fibqy>

Zhao F.Wang T.2001b, Some identities for the generalized Fibonacci and Lucas functions, Fibonacci Quart. 2001 (39,5): 436-438, fibqy>

Zhou1996, On the kth-order derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quart. 1996 (34,5): 394-408, fibqy>

Lucas-Bernoulli

KeepersYoung2008-09, On higher order Lucas-Bernoulli numbers, Fibonacci Quart. 2008-09 (46-47,1): 26-31, fibqy>

Lucasian

HiltonPedersenSomer1997, On Lucasian numbers, Fibonacci Quart. 1997 (35,1): 43-47, fibqy>

Somer2004, A further note on Lucasian numbers, Proc. 10th Int. Research Conf. on Fibonacci nbs. and their Applications Vol. 9: 225-234, gen>

Mahonian pairs, statistics

BabsonSteingrimsson2000, Generalized permutation patterns and a classication of the Mahonian statistics, Sém. Lothar. Combin (2000) Vol. 44, page B44b, 18 p, gen>

Burstein2015, On the distribution of some Euler-Mahonian statistics, J. Comb. Vol. 6, Number 3, 273–284, 2015, jou>

DelfertEinzigerRawlings2003, The derangement problem relative to the Mahonian process, Int. J. Math. Math. Sci. Vol. 2003 (2003), Issue 24, 1497-1508, gen>

GalovichWhite2007, Mahonian Z Statistics, Discrete Math. 307 (2007) 2341–2350, gen>

SaganSavage2011, Mahonian pairs, J. Combin. Theory Ser. A, Vol. 119, Issue 3, Apr 2012, 526-545, jou>

Wilson2010, An interesting new Mahonian permutation statistic, arXiv (21 Jul 2010), aXv>

Meixner

Alvarez-NodarseMarcellan1995b, Difference equation for modifications of Meixner polynomials, J. Math. Anal. Appl. Vol. 194, Issue 1, Aug 1995, 250–258, jou>

BarryHennessy2010b, Meixner-type results for Riordan arrays and associated integer sequences, J. Integer Seq. Vol. 13 (2010), Article 10.9.4, jis>

Bavinck, van Haeringen1994, Difference equations for generalized Meixner polynomials, J. Math. Anal. Appl. Vol. 184, Issue 3, Jun 1994, 453–463, jou>

BozejkoDemni2010, Topics on Meixner families, Banach Center Publications, 2010 Vol. 89, 61-74, nat>

BrycWesolowski2004, Conditional moments of q-Meixner processes, arXiv (13 Dec 2004), aXv>

GriffithsSpano2011, Multiv. Jacobi and Laguerre polyn., infinite-dimens. extensions and their prob. connect. with multiv. Hahn and Meixner polynomials, Bernoulli 17 (3), 2011, 1095–1125, gen>

KhanAkhlaq2012, A note on generating functions and summation formulas for Meixner polynomials of several variables, Demonstratio Math. Vol. XLV, No. 1, 2012, gen>

Shibukawa2014, Multivariate Meixner, Charlier and Krawtchouk polynomials, arXiv (29 Apr 2014), aXv>

Mellin

Coffey2006, Special functions and the Mellin transforms of Laguerre and Hermite functions, arXiv ( 28 Dec 2006), aXv>

FlajoletGourdonDumas1995, Mellin transforms and asymptotics: Harmonic sums, Theoret. Comput. Sci. 144 (1995), 3-58, gen>

 Oosthuisen2011, The Mellin transform, This project is supported by the National Research Foundation (NRF) (2011), gen>

ménage problem

Alekseyev2015, Weighted de Bruijn graphs for the Menage Problem and Its generalizations, arXiv (27 Oct 2015), aXv>

BogartDoyle1985, Non-sexist solution of the menage problem, The American Mathematical Monthly, Vol. 93, No. 7 (Aug. - Sep., 1986), 514-518, nat>

Borges2010, O Problema de Lucas-Ménage Probleme, Universidade Federal do Piau 28 de setembro de 2010, gen>

Holst1991, On the ‘problčme des ménages’ from a probabilistic viewpoint, Statist. Probab. Lett. Vol. 11, Issue 3, March 1991, 225-231, gen>

Kaplansky I.1943, Solution of the “Problčme des ménages”, Bull. Amer. Math. Soc. 49 (1943), 784–785, nat>

Neuschel2012, Asymptotics for ménage polynomials and certain hypergeometric polynomials of type 3F1, J. Approx. Theory 164 (2012), 981–1006, jou>

Qureshi2007, A new version of the ménages problem, arXiv (24 May (2007), aXv>

Takacs1981, On the "Problčme des Ménages", Discrete Math. 36 (1981) 289 – 297, gen>

WymanMoser1958.pdf, On the problčme des ménages, Canad. J. Math. 10 (1958), 468-480, nat>

Zeilberger2014, Automatic énumeration of generalized ménage numbers, Séminaire Lotharingien de Combinatoire 71 (2014), Article B71a, gen>

mixed-type polynomials

Kim D.S.Kim T.KwonSeo2014, Identities of some special mixed-type polynomials, Adv. Studies Theor. Phys. Vol. 8, 2014, no. 17, 745-754, gen>

KimKim2013c, Higher -order Cauchy of the first kind and poly-Cauchy of the first kind mixed type polynomials, arXix (9 Aug 2013), aXv>

modular

Hilbert

Wierstrass

modular curves

modular forms

modular functions

moments

AlbeverioHerzberg2008, The moment problem on the Wiener space, Bull. Sci. math. 132 (2008) 7–18, nat>

Barry2011a, Riordan arrays, orthogonal polynomials as moments, and Hankel transforms, J. Integer Seq. Vol. 14 (2011), Article 11.2.2, jis>

Barry2011c, Combinatorial polynomials as moments, Hankel transforms, and exponential Riordan arrays, J. Integer Seq. Vol. 14 (2011), Article 11.6.7, jis>

Barry2011d, Eulerian polynomials as moments, via exponential Riordan arrays, J. Integer Seq. Vol. 14 (2011), Article 11.9.5, jis>

Barry2013e, General Eulerian polynomials as moments using exponential Riordan arrays, J. Integer Seq. Vol. 16 (2013), Article 13.9.6, jis>

Barry2013g, Comparing two matrices of generalized moments defined by continued fraction expansions, arXiv (27 Nov 2013), aXv>

Barry2014c, Embedding structures associated with Riordan arrays and moment matrices, Int. J. Comb. Vol. 2014 (2014), Article ID 301394, 7 p, gen>

BarryHennessy2010a, The Euler-Seidel matrix, Hankel matrices and moment sequences, J. Integer Seq. Vol. 13 (2010), Article 10.8.2, jis>

BelbachirRahmaniSury2011, Sums involving moments of reciprocals of binomial coefficients, J. Integer Seq. Vol. 14 (2011), Article 11.6.6, jis>

BrycWesolowski2004, Conditional moments of q-Meixner processes, arXiv (13 Dec 2004), aXv>

ChenChu2009, Moments on Catalan numbers, J. Math. Anal. Appl. Vol. 349, Issue 2, 15 Jan 2009, 311–316, jou>

Di NardoSenato2006, An umbral setting for cumulants and factorial moments, European J. Combin. Vol. 27, Issue 3, Apr 2006, 394–413, gen>

Diaconis1986, Application of the method of moments in probability and statistics, Technical Report 262, Stanford Univ. Stanford-California, 1986, gen>

Dubois-Violette2015, Lectures on the classical moment problem and its noncommutative generalization, arXiv (5 Nov 2015), aXv>

Fasino1995, Spectral properties of Hankel matrices and numerical solutions of finite moment problems, J. Comp. Appl. Math. 65 (1995) 145-155, jou>

IsmailStanton1997, Classical Orthogonal Polynomials as moments, Can. J. Math. Vol. 49 (3), 1997, 520–542, nat>

IsmailStanton1998, More orthogonal polynomials as moments, Progr. Math. Vol. 161, 1998, 377-396, gen>

Kjeldsen1993, The early history of the moment problem, Historia Mathematica, Vol. 20, Issue 1, Feb 1993, 19–44, gen>

Landau1980, The classical moment problem : Hilbertian proofs, J. Funct. Anal. 38, 255-272 (1980), jou>

MizrahiGaletti2002, Laguerre moments and generalized functions, J. Phys. A: Math. Gen. 35 (2002) 3535–3546, jou>

Schmüdgen1987, On a generalization of the classical moment problem, J. Math. Anal. Appl. Vol. 125, Issue 2, August 1987, 461–470, jou>

Soundrarajan2009, Moments of the Riemann z-function, Ann. of Math. (2), 170 (2009), 981–993, nat>

Štampachxxxx, The moment problem, Seminar-Faculty of Nuclear Sciences and Physical Engineering, CTU Prague xxxx, gen>

Steere2012, Orthogonal polynomials and the moment problem, Faculty of Science, University of the Witwatersrand, Johannesburg, 2012, Master of Science, gen>

Sulanke2000, Moments of generalized Motzkin paths, J. Integer Seq. Vol. 3 (2000), Article 00.1.1, jis>

Tesko2011, One generalization of the classical moment problem, Methods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 356–380, gen>

Morgan-Voyce

André-Jeannin1994b, A generalization of Morgan-Voyce polynomials, Fibonacci Quart. 1994 (32,3): 228-231, fibqy>

Horadam1996c, Polynomials associated with generalized Morgan-Voyce polynomials, Fibonacci Quart. 1996 (34,4):  342-348, fibqy>

Swamy2000, Generalizations of Modified Morgan-Voyce Polynomials, Fibonacci Quart. 2000 (38,1): 8-16, fibqy>

Motzkin

Aigner1998, Motzkin numbers, European J. Combin. Vol. 19, Issue 6, Aug. 1998, 663–675, gen>

Arreghi2001a, Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles, arXiv (17 Sept 2001), aXv>

BarcucciPinzaniSprugnoli1991, The Motzkin family, PU.M.A. Pure Mathematics and Applications Ser. A, 2 (1991), No. 3-4: 249-279, gen>

Bernhart1999, Catalan, Motzkin, and Riordan numbers, Discrete Math. Vol. 204, Issues 1–3, 6 Jun 1999, 73–112, gen>

BlasiakDattoliHorzelaPensonZhukovsky2008, Motzkin numbers, central trinomial coefficients and hybrid polyn., J. Integer Seq. Vol. 11 (2008), Article 08.1.1, jis>

CameronYip2011, Hankel determinants of sums of consecutive Motzkin numbers, Linear Algebra Appl Vol. 434, Issue 3, 1 Feb 2011, 712–722, gen>

DengYan2008, Some identities on the Catalan, Motzkin and Schröder numbers, Discrete Appl. Math. Vol. 156, Issue 14, Jul 2008, 2781–2789, gen>

DeutschSagan2006, Congruences for Catalan and Motzkin numbers and related sequences, J. Number Theory Vol. 117, Issue 1, Mar 2006, 191–215, jou>

DonagheyShapiro1977, Motzkin numbers, J. Combin. Theory Ser. A, Vol. 23, Issue 3, Nov 1977, 291–301, jou>

EuLiuYeh2008, Catalan and Motzkin numbers modulo 4 and 8, European J. Combin. Vol. 29, Issue 6, Aug 2008, 1449–1466, gen>

MansourSchorkSun2007, Motzkin numbers of higher rank: generating function and explicit expression, J. Integer Seq., Vol. 10 (2007), Article 07.7.4, jis>

Romik2003, Some formulas for the central trinomial and Motzkin number, J. Integer Seq. Vol. 6 (2003), Article 03.2.4, jis>

SteinWaterman1978, On some sequences generalizing the Catalan and Motzkin numbers, Discrete Math. Vol. 26, Issue 3, Jan 1979, 261-272, gen>

Sulanke2000, Moments of generalized Motzkin paths, J. Integer Seq. Vol. 3 (2000), Article 00.1.1, jis>

Wang YiZhang Z-H.2015, Combinatorics of generalized Motzkin numbers, J. Integer Seq. Vol. 18 (2015), Article 15.2.4, jis>

Narayana

Barry2011b, On a generalization of the Narayana triangle, J. Integer Seq. Vol. 14 (2011), Article 11.4.5, jis>

BarryHennessy2011, A note on Narayana triangles and related polynomials, Riordan arrays, and MIMO capacity calculations, J. Integer Seq. Vol. 14 (2011), Article 11.3.8, jis>

MansourSun2009, Identities involving Narayana polynomials and Catalan numbers, Discrete Math. Vol. 309, Issue 12, Jun 2009, 4079–4088, gen>

PetkovicBarryRajkovic2012, Closed-form expression for Hankel determinants of the Narayana polynomials, Czechoslovak Math. J. 62 (137) (2012), 39–57, nat>

PetkovicRajkovic2006, Hankel transform of Narayana polynomials and generalized Catalan numbers, Int. Conference PRIM 2006, gen>

Narumi

Kim D.S.Kim T.2014a, Barnes-type Narumi polynomials, Adv. Difference Equ. 2014, 2014: 182, gen>

n-bonacci numbers

 Lee J-Z.Lee J-S.1987, A complete characterization of B-power fractions that can be represented as series of of general n-bonacci numbers, Fibonacci Quart. 1997 (25,1): 72-75, fibqy>

Newton series

ZengZhang1994, A q-analog of Newton’s series, Stirling functions and Eulerian functions, Results Math. May 1994, Vol. 25, Issue 3-4, 370-391, gen>

Norlund

Adelberg1998, 2-adic congruences of Nörlund numbers and of Bernoulli numbers of the second kind, J. Number Theory 73, 47-58 (1998), jou>

Adelberg1999, Arithmetic properties of the Nörlund polynomial B^( x)n, Discrete Math. 204 (1999) 5-13, gen>

Bencherif2010, Sur une propriété des polynômes de Nörlund, Actes des rencontres du C.I.R.M. Vol. 2 no 2 (2010), 71-77, gen>

Carlitz1960a, Note on Norlund's polynomial B^(z)_n, Proc. Amer. Math. Soc. Vol. 11, No. 3 (Apr 1960), 452-455, nat>

Carlitz1967, Some properties of the Nórlund polynomial Bn(x), Mathematische Nlachrichten Volurne Vol. 33, Issue 5-6, 297–311, 1967, gen>

LiuSrivastava2006, Explicit formulas for the Nordlund polynomial Bn(x) and bn(x), Comput. Math. Appl. Vol. 51, Issues 9–10, May 2006, 1377–1384, gen>

Steffensen1926, On a generalization of Nordlund's polynomials, Det Kgl . Danske Videnskabernes Selskab . Mathematisk-fysiske Meddelelser . VII, 5., gen>

Norlund-Bernoulli

Zhang Z.1998, Recurrence sequences and Nordlund-Bernoulli polynomials, Math. Morav. Vol. 2 (1998), 161-168, nat>

Norlund-Euler

TianmingZhizheng1996, Recurrence sequences and Nörlund-Euler polynomials, Fibonacci Quart. 1996 (34,4): 314-319, fibqy>

operational calculus

Abdlhusein2014, The Euler operator for basic hypergeometric series, Int. J. Adv. Appl. Math. and Mech. 2 (1) (2014), 42-52, gen>

Abramov R.V.2010, The multidimensional maximum entropy moment problem: A review on numerical methods, Commun.  math. sci. 8(2010) · June 2010, gen>

Abramov2003, When does Zeilberger’s algorithm succeed?, Adv. in Appl. Math. 30 (2003) 424–441, gen>

Adukov1999, Generalized inversion of finite rank Hankel and Toeplitz operators with rational matrix symbols, Linear Algebra App 290 (1999) 119 134, gen>

AharmimHamyaniWassouliGhanmi2013, New operational formulas and generating functions for the generalized Zernike polynomials, arXiv (12 Dec 2013), aXv>

Al-Salam1984, Some operational formulas for the g-Laguerre polynomials, Fibonacci Quart. 1984 (22,2): 166-170, aXv>

Al-Salam1989, On some q-operators with applications, Indag.Math. (N.S.) (Proceedings), Vol. 92, Issue 1, Mar 1989, 1–13, gen>

BasorEhrhardt1999, On a class of Toeplitz + Hankel operators, New York J. Math. 5 (1999) 1-16, nat>

Bavinck1998, Differential and difference operators having orthogonal polynomials with two linear perturbations as eigenfunctions, J. Comp. Appl. Math.Vol. 92, Issue 2, 26 Jun 1998, 85–95, jou>

Belbahri2010, Scale invariant operators and combinatorial expansions, Adv. in Appl. Math. Vol. 45, Issue 4, Oct 2010, 548–563, gen>

BojdiAhmadi-AslAminataei2013, Operational matrices with respect to Hermite polyn. and their applications in solving linear differential equations with variable coeff., J. of Linear and Topological Algebra Vol. 02, No. 02, 2013, 91-103, jou>

Bouaziz1993, Testing Gaussian sequences and asymptotic inversion of Toeplitz operators, Probab. Math. Statist. Vol. 14, Fasc. 2 (1993), p 207-222, gen>

Cao2010, Notes on Carlitz’s q-operators, Taiwanese J. Math. Vol. 14, No. 6, 2229-2244, Dec 2010, nat>

Cardenas-MoralesGarrancoRasa2011, Bernstein-type operators which preserve polynomials, Comput. Math. Appl. 62 (2011) 158–163, gen>

Carlitz1973, Eulerian numbers and operators, Lecture Notes in Math. 1971, 65-70 -The Theory of Arith. Funct., gen>

CarlitzScoville1975, Eulerian numbers and operators, Fibonacci Quart. 1975 (13,1): 71-83, fibqy>

Chapoton2011, q-analogues of Bernoulli numbers & zeta operators at negative integers, CNRS et Université Claude Bernard Lyon 1, nat>

Chatterjea1963a, Operation formulae for certain classical polynomials (I), Q. J. Math. vol. 14, no. 1, pp. 241-246, 1963, gen>

Chatterjea1963b, Operational formulae for certain classical polynomials-II, Rend. Semin. Mat. Univ. Padova, 1963, Vol. 33, 163-169, nat>

Chatterjea1963c, Operational formulae for certain classical polynomials-III, Rend. Semin. Mat. Univ. Padova, 1963, Vol. 33, 271-277, gen>

ChatterjeaSrivastava1993, A unified presentation of certain operational formulas for the Jacobi and related polynomials, Applied Math. and Computation, Vol. 58, Issue 1, 15 Sep 1993, 77-95, gen>

ChenGu2008, The Cauchy operator for basic hypergeometric series, Adv. in Appl. Math. Vol. 41, Issue 2, Aug 2008, 177–196, gen>

ChenSaadSun2009, An operator approach to the Al-Salam-Carlitz polynomials, arXiv (9 Oct 2009), arXiv>

Costas-Santos2006, The characterization theorems and the Rodrigues operator. A general approach, DGES grant BFM 2003-06335-C03 Almer´ıa, Aug 31, 2006 Universidad Carlos III de Madrid, nat>

DancsHe2013, q-analogues of symbolic operators, J. of Discrete Math. Vol. 2013 (2013), Article ID 487546, 6 p, jou>

Dattoli2000, Generalized polynomials, operational identities and their applications, J. Comp. Appl. Math. Vol. 118, Issues 1–2, Jun 2000, 111–123, jou>

DattoliLorenzuttaManchoTorre1999, Generalized polynomials and associated operational identities, J. Comp. Appl. Math. Vol. 108, Issues 1–2, Aug 1999, 209–218, jou>

Ehrhardt2004, Factorization theory for Toeplitz plus Hankel operators and singular integral operators with flip, Thesis, Fakult¨at f¨ur Mathematik, Technische Universit¨at Chemnitz, 2004,

Ernst2004, q-analogues of some operational formulas, U.U.D.M. Report 2004: 4, gen>

Ernst2009, q-calculus as operational algebra, Proc. Est. Acad. Sci. 2008, 58, 2, 73-97, nat>

Ghanmi2013, Operational formulae for the complex Hermite polynomials Hp,q(z, z^), arXiv (10 Jan 2013), aXv>

Gould1963, Operational recurrences involving Fibonacci numbers, Fibonacci Quart. 1963 (1,1):  30-33, fibqy>

Halberg, Jr.1968, The generalized Fibonacci operator, The Fibonacci Quarterly 1968 (6,5):  15-33, fibqy>

He2008, A symbolic operator approach to power series transformation-expansion formulas, J. Integer Seq. Vol. 11 (2008), Article 08.2.7, jis>

HeHsuShiue2006, Convergence of the summation formulas constructed by using a symbolic operator approach, Comput. Math. Appl. Vol. 51, Issues 3–4, Feb 2006, 441–450, gen>

HeHsuShiue2008, A symbolic operator approach to several summation formulas for power series II, Discrete Math. Vol. 308, Issue 16, 28 Aug 2008, 3427–3440,

HeHsuShiueTorney2005, A symbolic operator approach to several summation formulas for power series, J. Comp. Appl. Math. Vol. 177, Issue 1, 1 May 2005, 17–33, jou>

HeHsuYin2009, A pair of operator summation formulas and their applications, Comput. Math. Appl. Vol. 58, Issue 7, Oct 2009, 1340–1348, gen>

IbrahimDarus2011, On operator defined by double zeta functions, Tamkang J. Math. Vol. 42, No. 2, 163-174, Summer 2011, nat>

Ismail2001, An operator calculus for the Askey-Wilson operator, Ann. Comb. Dec 2001, Vol. 5, Issue 3-4, 347-362, gen>

Khan1995, On some operational representations of q-polynomials, Czechoslovak Math. J. Vol. 45 (1995), No. 3, 457--464, nat>

Krattenthaler1988, Operator methods and Lagrange inversion: a unified approach to Lagrange formulas, Trans. Amer. Math. Soc. Vol. 305, No. 2, Feb 1988, 431-465, nat>

Kwasniewski2004a, Towards psi −extension of finite operator calculus of Rota, arXiv (5 Feb 2004), ), aXv>

Nash1976, Some operational formulas, Fibonacci Quart. 1976 (14,1): 1-8, fibqy>

ÖksüzerKarsliYesildal2015, Order of approximation by an operator involving biorthogonal polynomials, J. Inequal. Appl. (2015) 2015: 121, jou>

PatilThakare1976a, New operational formulas and generating functions for Laguerre polynomials, Indian J. Pure Appl. Math. 1976 (7,10): 1104-1118, nat>

PhadkeThakare1979, Generalized inverses and operator equations, Linear Algebra Appl Vol. 23, Feb 1979, 191–199, gen>

Robin2012, On the Rodrigues’ formula approach to Operator factorization, Int. Mathematical Forum, Vol. 7, 2012, no. 47, 2333 - 2351, gen>

RotaKahanerOdlyzko1973, On the foundations of combinatorial theory. VIII. Finite operator calculus, J. Math. Anal. Appl. Vol. 42, Issue 3, Jun 1973, 684–760, jou>

SaadSukhi2013, The q-exponential operator, Appl. Math. Sci. (Ruse) Vol. 7, 2013, no. 128, 6369-6380, gen>

Singhal1967, Operational formulae for certain classical polynomials, Rend. Semin. Mat. Univ. Padova, tome 38 (1967), 33-40, nat>

SrivastavaSinghSingh1979, Operational derivation of generating functions of a generalized function, Indian J. Pure Appl. Math. 10 (3), 326-328, Mar 1979, nat>

ZhangWuyungaowaMa2013, A class of formal operators for combinatorial identities and its application, Int. J. of Mathematical, Comput., Physical and Quantum Engineer. Vol. 7, No:3, 2013, gen>

Oresme

Cook2004, Some sums related to sums of Oreme numbers, Proc. of the 10th Int. Conf. on Fibonacci nbs. and their Appl. 2004, Vol. 9, 87-99, gen>

Horadam1974a, Oresme numbers, The Fibonacci Quarterly 1974 (12,3): 267-270, fibqy>

orthogonal (q-)polynomials

AharonovBeardonDriver2005, Fibonacci, Chebyshev, and orthogonal polynomials, Amer. Math. Monthly Vol. 112, No. 7 (2005), 612-630, nat>

AndrewsWimp2002, Some q-orthogonal polynomials and related Hankel determinants, Rocky Mountain J. Math. Vol. 32, No. 2, Summer 2002, nat>

Askey2005, Duality for classical orthogonal polynomials, J. Comp. Appl. Math. Vol. 178, Issues 1–2, 1 Jun 2005, 37–43, jou>

AtakishiyevKlimyk2004, On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials, J. Math. Anal. Appl. Vol. 294, Issue 1, Jun 2004, 246-257, jou>

Barry2013f, Laurent biorthogonal polynomials and Riordan arrays, arXiv (10 Nov 2013), aXv>

BarryHennessy2012a, Four-term recurrences, orthogonal polynomials and Riordan arrays, J. Integer Seq., Vol. 15 (2012), Article 12.4.2, jis>

Bavinck1998, Differential and difference operators having orthogonal polynomials with two linear perturbations as eigenfunctions, J. Comp. Appl. Math.Vol. 92, Issue 2, 26 Jun 1998, 85–95, jou>

Ben CheikhBen Romdhane2011, On d-symmetric classical d-orthogonal polynomials, J. Comp. Appl. Math. Vol. 236, Issue 1, 1 Aug 2011, 85–93, jou>

Ben CheikhLamiriOuni2009, On Askey-scheme and d-orthogonality, I: A characterization theorem, J. Comp. Appl. Math. Vol. 233, Issue 3, 1 Dec 2009, 621–629, jou>

Ben CheikhOuni2008, Some generalized hypergeometric d-orthogonal polynomial sets, J. Math. Anal. Appl. Vol. 343, Issue 1, Jul 2008, 464–478, jou>

Berg2011, Fibonacci numbers and orthogonal polynomials, Arab J. Math. Sci. Vol. 17, Issue 2, Jul 2011, 75–88, nat>

BertolaGekhtmanSzmigielski2010, Cauchy biorthogonal polynomials, J. Approx. Theory Vol. 162, Issue 4, Apr 2010, 832–867, jou>

BultheelCuyt Van AsscheVan BarelVerdonk2005, Generalizations of orthogonal polynomials, J. Comp. Appl. Math. Vol. 179, Issues 1–2, 1 Jul 2005, 57–95, jou>

CanteroIserles2013, On expansions in orthogonal polynomials, Adv. Comput. Math. 2013, Volume 38, Issue 1, 35-61, gen>

ChammamMarcellanSfaxi2012, Orthogonal polynomials, Catalan numbers, and a general Hankel determinant evaluation, Linear Algebra Appl Vol. 436, Issue 7, Apr 2012, 2105-2116, gen>

ChenSrivastava1995, Orthogonality relations and generating functions for Jacobi polynomials and related hypergeometric functions, Appl. Math. Comput. Vol. 68, Issues 2–3, 15 Mar 1995, 153–188, gen>

CorteelJosuat-VergčsWilliams2010, The matrix ansatz, orthogonal polynomials, and permutations, arXiv (15 May 2010), aXv>

Costas-Santos2006, The characterization theorems and the Rodrigues operator. A general approach, DGES grant BFM 2003-06335-C03 Almer´ıa, Aug 31, 2006 Universidad Carlos III de Madrid, nat>

Costas-SantosMarcellan2010, q-Classical orthogonal polynomials: A general difference calculus approach, Acta Appl. Math. Jul 2010, Vol. 111, Issue 1, 107-128 arXiv (23 Jun 2009), gen>

DamanikPushmitskiSimon 2008, The analytic theory of matrix orthogonal polynomials, Surv. Approx. Theory, Vol. 4, 2008, 1–85, gen>

Della Riccia2008, Riordan arrays, Sheffer sequences and “Orthogonal” Polynomials, J. Integer Seq. Vol. 11 (2008), Article 08.5.3, jis>

DombrowskiNevai1986, Orthogonal polynomials, measures and recurrence relations, SIAM J. Math. Anal. 1986, Vol. 17, No. 3 : 752-759, gen>

DumitriuEdelmanShuman2004, MOPS: Multivariate orthogonal polynomials (symbolically), J. Symbolic Comput. 42 (2007), 587–620, jou>

FoupouagnigniRonveauxKoepf1998, Fourth order q-difference equation for the first associated of the q-classical orthogonal polynomials, J. Comp. Appl. Math. Vol. 101, Issues 1–2, Jan 1999, 231–236, jou>

GhressiKhérijiTounsi2011, An introduction to the q-Laguerre-Hahn orth. q-polyn., SIGMA Symmetry Integrability Geom. Methods Appl. 7 (2011), 092, 20 p, gen>

Grandati2013, Exceptional orthogonal polynomials and generalized Schur polynomials, arXiv (18 Nov 2013), aXv>

Hennessy2011, A study of Riordan arrays with applications to continued fractions, orthogonal polynomials and lattice paths, Thesis-Waterford Institute of Technology (Oct 2011), gen>

HoungaHounkonnouRonveaux2006, New families of orthogonal polynomials, J. Comput. Appl. Math. Vol. 193, Issue 2, Sept 2006, 474–483, jou>

HussainSingh1979, Mixed generating relations for polynomials related to Konhauser biorth. Polyn., Port. Math. 1979, Vol. 38, Issue: 3-4, 181-187, nat>

HussainSingh1980, Some properties of orthogonal polynomials related to Hermite polynomials, Indian J. Pure Appl. Math. 11(8): 1018-1020, Aug 1980, nat>

IserlesNorsett1988, On the theory of biorthogonal polynomials, Trans. Amer. Math. Soc. Vol. 306, No. 2 (Apr., 1988), 455-474, nat>

IsmailStanton1997, Classical Orthogonal Polynomials as moments, Can. J. Math. Vol. 49 (3), 1997, 520–542, nat>

IsmailStanton1998, More orthogonal polynomials as moments, Progr. Math. Vol. 161, 1998, 377-396, gen>

KarandePatil1981, Expansion formulas for Srivastava polynomials in series of the Konhauser biorthogonal polynomials, Indian J. Pure Appl. Math. 12(9):1124-1128, Sep 1981, nat>

KoekoekLeskySwarttouw2013, Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics 2013, gen>

KoepfSchmersau1998, Representations of orthogonal polynomials, J. Comp. Appl. Math. Vol. 90, Issue 1, Apr 1998, 57–94, jou>

Konhauser1967, Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. Vol. 21, No. 2, 1967, nat>

Koornwinder1988, Group theoretic interpretation of Askey's scheme of hypergeometric orthogonal polynomials, Lecture Notes in Math. Vol. 1329, 1988, 46-72, gen>

Koornwinder2014, Additions to the formula lists in "Hypergeometric orthogonal polynomials and their q-analogues" by Koekoek, Lesky and Swarttouw, arXiv (4 Jan 2014), aXv>

KoornwinderOnn2006, LU factorizations, q = 0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials, Ramanujan J. Vol. 13, Issue 1-3, (Jun 2007), 365-387, aXv>

KwonLittlejohn1997, Classification of classical orthogonal polynomials, J. Korean Math. Soc. 34 (1997), No. 4, 973–1008, nat>

Lehner2003, Cumulants, lattice paths, and orthogonal polynomials, Discrete Math. Vol. 270, Issues 1–3, Aug 2003, 177–191, gen>

MadhekarThakare1982, Biorthogonal polynomials suggested by the Jacobi polynomials, Pacific J. Math. Vol. 100, No. 2 (1982), 417-424, nat>

MarcellanMedem1999, Q−classical orthogonal polynomials: a very classical approach, Electron. Trans. Numer. Anal. Vol. 9, 1999, 112-127, gen>

MeijerPimar2003, A generating function for Laguerre–Sobolev orthogonal polynomials, J. Approx. Theory Vol. 120, Issue 1, Jan 2003, 111–123, jou>

MorenoGarcia-Caballero2011a, q-Sobolev orthogonality of the q-Laguerre polynomials Ln^(-N) ( ; q)n =0^ for positive integers N, J. Korean Math. Soc. 48 (2011), No. 5, 913-926, nat>

OdakeSasaki2008, Orthogonal polynomials from Hermitian matrices, arXiv (27 feb 2008), aXv>

ÖksüzerKarsliYesildal2015, Order of approximation by an operator involving biorthogonal polynomials, J. Inequal. Appl. (2015) 2015: 121, jou>

PérezPinar1996, On Sobolev orthogonality for the generalized Laguerre polynomials, J. Approx. Theory Vol. 86, Issue 3, Sep 1996, 278–285, jou>

Shah1972, On some results on H-functions associated with orthogonal polynomials, Math. Scand. 30 (1972), 331-336, nat>

Shen2000, Orthogonal polynomials on the unit circle associated with the Laguerre polynomials, Proc. Amer. Math. Soc. (2000) 129, No. 3, 873–879, nat>

Steere2012, Orthogonal polynomials and the moment problem, Faculty of Science, University of the Witwatersrand, Johannesburg, 2012, Master of Science, gen>

Szablowski2013, On the q-Hermite polynomials and their relationship with some other families of orth. polyn., Demonstratio Math. Vol. XLVI No 4 2013, gen>

Szwarc1992, Connection coefficients of orthogonal polynomials, Canad. Math. Bull. Vol. 35 (4), 1992, 548-556, nat>

ThakareMadhekar1988, A pair of biorthogonal polynomials for the Szego-Hermite weight function, Int. J. Math. Math. Sci. Vol. 11 No. 4 (1988), 763-768, gen>

 

Van AsscheCoussement2001, Some classical multiple orthogonal polynomials, J. Comp. Appl. Math.. Vol. 127, Issues 1–2, 15 Jan 2001, 317–347, jou>

Viennot1983, Une théorie combinatoire des polynômes orthogonaux généraux, Notes de conférences données ŕ l’Univ. du Québec ŕ Montréal, gen>

partial Euler product

FarmerKoutsoliotasLemurellZubairy2008, Modular forms and L-functions with a partial Euler product, xxxx, gen>

FarmerWilson2008, Converse theorems assuming a partial Euler product, The Ramanujan J. Feb 2008, Vol. 15, Issue 2, p 205-218, gen>

Lemurell2008, Modular forms and L-functions with a partial Euler product, J. Ramanujan Math. Soc., Vol.23, Issue 2, 2008, 105-121, jou>

Pascal

Barry2013b, A note on a family of generalized Pascal matrices defined by Riordan arrays, J. Integer Seq. Vol. 16 (2013), Article 13.5.4, jis>

Barry2013c, On the inverses of a family of Pascal-like matrices defined by Riordan arrays, J. Integer Seq. Vol. 16 (2013), Article 13.5.6, jis>

BelbachirKomatsuSzalay2014, Linear recurrences associated to rays in Pascal's triangle and combinatorial identities, Math. Slovaca 64 (2014), No. 2, 287-300, nat>

Bollinger1984, Fibonacci k-sequences, Pascal-T triangles, and k-in-a-row problems, Fibonacci Quarterly 1984 (22,2): 146-151, fibqy>

BoothNguyen2008-09, Bernoulli polynomials and Pascal’s square, Fibonacci Quart. 2008-09 (46-47,1): 38-47, fibqy>

CallVelleman1993, Pascal's Matrices, The Amer. Math. Month.Vol. 100, No. 4 (Apr., 1993), p 372-376, nat>

EdelmanStrang2004, Pascal matrices, Amer. Math. Monthly, 111 (2004), 189-197, nat>

Edwards2008-09, A Pascal-like triangle related to the tribonacci numbers, Fibonacci Quart. 2008-09 (46-47,1): 18-25, fibqy>

Ernst2008b, q-Pascal and q-Bernoulli matrices, an umbral approach, U.U.D.M. Report 2008: 23, gen>

Hoggatt, Jr.Bicknell1976d, Catalan and related sequences arising from inverses of Pascal's triangle matrices, Fibonacci Quart. 1976 (14,5): 395-404, fibqy>

J. Pita Ruiz V.2013, Some number arrays related to Pascal and Lucas triangles, J. Integer Seq. Vol. 16 (2013), Article 13.5.7, jis>

Koshy2011, Fibonacci, Lucas, and Pell numbers, and Pascal’s triangle, Mathematical Spectrum 2010/2011, Vol. 43 Issue 3, 125, gen>

Rogers1978, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math. Vol. 22, Issue 3, 1978, 301-310, gen>

Szablowski2014, A few remarks on Euler and Bernoulli polyn. and their connections with binom. coef. and modified Pascal matrices, Math. Ćterna, Vol. 4, 2014, no. 1, 83-88, gen>

Velasco2013, Some number arrays related to Pascal and Lucas triangles, J. Integer Seq. Vol. 16 (2013), Article 13.5.7, jis>

WasutharatKuhapatanakul2012, The generalized Pascal-like triangle and applications, Int. J. Contemp. Math. Sci. Vol. 7, 2012, no. 41, 1989-1992, gen>

Yang S-L.You2007, On a connection between the Pascal, Stirling and Vandermonde matrices, Discrete Applied Math. Vol. 155, Issue 15, Sep 2007, 2025-2030, gen>

Zhang Z.Wang X.2007, A factorization of the symmetric Pascal matrix involving the Fibonacci matrix, Discrete Appl. Math. Vol. 155, Issue 17, Oct 2007, 2371-2376, gen>

Zhizheng Z.1997, The linear algebra of the generalized Pascal matrix, Linear Algebra Appl. Vol. 250, Jan 1997, 51-60, gen>

paths

Arreghi2001b, Bernoulli and Euler numbers, Motzkin paths and numerical triangles, Pre-publicaciones del Seminario Matemático "García de Galdeano", Nş. 34, 2001, gen>

ChenDengYang2008, Riordan paths and derangements, Discrete Math. Vol. 308, Issue 11, Jun 2008, 2222–2227, gen>

ChengEuFu2007, Area of Catalan paths on a checkerboard, European J. of Combin. Vol. 28, Issue 4, May 2007, 1331–1344, gen>

ElizaldeMansour2005, Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials, Discrete Math. 305 (2005) 170–189, gen>

KauersZeilberger2011, The computational challenge of enumerating high-dimensional rook walks, Adv. in Appl. Math. Vol. 47, Issue 4, (Oct 2011), 813–819, gen>

Nkwanta2009, Lattice path and RNA secondary structure predictions, 15th Conf. African American Researchers Math. Sci.-Rice Univ., Jun 23-26, 2009, gen>

NkwantaShapiro2005, Pell walks and Riordan matrices, Fibonacci Quart. 2005 (43,2): 170-180, fibqy>

Sulanke2000, Moments of generalized Motzkin paths, J. Integer Seq. Vol. 3 (2000), Article 00.1.1, jis>

Sun Y.Ma2014b, Minors of a class of Riordan arrays related to weighted partial Motzkin paths, Europ. J. Combin. Vol. 39, Jul 2014, 157–169 arXiv (9 May 2013), aXv>

Woan2001, Hankel matrices and lattice paths, J. Integer Seq. Vol. 4 (2001), Article 01.1.2, jis>

Yan2007, From (2, 3)-Motzkin paths to Schroder paths, J. Integer Seq. Vol. 10 (2007), Article 07.9.1, jis>

patterns

BerniniBouvelFerreri2006 (1), Some statistics on permutations avoiding generalized patterns, GASCom 2006, Sep 2006, Dijon, France, gen>

BerniniBouvelFerreri2006 (2), Some statistics on permutations avoiding generalized patterns, arXiv (29 Nov 2006), aXv>

Elizalde2006, Asymptotic enumeration of permutations avoiding generalized patterns, Adv. Appl. Math. 36 (2006), 138–155, gen>

Krattenthaler2001, Permutations with restricted patterns and Dyck paths, Adv. Appl. Math. 27, 510–530 (2001), gen>

Rajaraman2012, Asymptotic behaviour of permutations avoiding generalized patterns, MATH 821-Final Projects Dec 2010, Simon Fraser University, gen>

RegevRoichman2005, Generalized statistics on Sn and pattern avoidance, European J. Combin. 26 (2005), 29–57, gen>

Robertson1999, Permutations containing and avoiding 123 and 132 patterns, arXiv (29 Mar 1999), aXv>

RobertsonWilfZeilberger1999, Permutation patterns and continued fractions, Electron. J. Combin. 6 (1999), #R38 2, jou>

Pell

de AndradeSantosda SilvaSilva2013, Polynomial generalizations and combinatorial interpretations for seq. including the Fibonacci and Pell numbers, Open J. of Discrete Math. 2013, 3, 25-32, gen>

DuvallVaughan1988, Pell polynomials and a conjecture of Mahon and Horadam, Fibonacci Quart. 1988 (26,4): 344-353, fibqy>

Horadam1994b, Maximal representations of positive integers by Pell numbers, Fibonacci Quart. 1994 (32,3): 240-244, fibqy>

HoradamMahon1985, Pell and Pell-Lucas polynomials, Fibonacci Quart. 1985 (23,1): 7-20, fibqy>

JhalaRathoreSisodiya2014a, Some determinantal identities involving Pell polynomials, Int. J. Scientific Innovative Math. Research Vol. 2, Issue 5, May 2014, 481-488, gen>

KiliçTasci2006, The generalized Binet formula, representation and sums of the generalized order-k Pell numbers, Taiwanese J. of Math. Vol. 10, No. 6, 1661-1670, Dec 2006, nat>

LuJang2013, The sum and product of Fibonacci numbs. and Lucas numbs., Pell numbs. and Pell-Lucas numbs. representation by matrix method, WSEAS Trans. on Math., Issue 4, Vol. 12, Apr 2013, gen>

MahonHoradam1987b, Ordinary generating functions for Pell polynomials, Fibonacci Quart. 1987 (25.1): 45-56, fibqy>

SantanaDiaz-Barrero2006, Some properties of sums involving Pell numbers, Missouri J. Math. Sci. 01/2006; 18(1), 33-40, nat>

ShannonHoradam2004, Generalized Pell numbers and polynomials, Proc. of the 10th Int. Conf. on Fibonacci nbs. and their Appl. 2004, Vol. 9, 213-224, gen>

Pell-Lucas

Dasdemir2011, On the Pell, Pell-Lucas and modified Pell numbers By matrix method, Appl. Math. Sci. Vol. 5, 2011, no. 64, 3173-3181, gen>

HoradamMahon1985, Pell and Pell-Lucas polynomials, Fibonacci Quart. 1985 (23,1): 7-20, fibqy>

LuJang2013, The sum and product of Fibonacci numbs. and Lucas numbs., Pell numbs. and Pell-Lucas numbs. representation by matrix method, WSEAS Trans. on Math., Issue 4, Vol. 12, Apr 2013, gen>

Pell equation, Pell-Abel equation

Halter-Koch2011, Diophantine equations of Pellian type, J. Number Theory Vol. 131, Issue 9, Sep 2011, 1597–1615, jou>

Pastor2001, Generalized Chebyshev polynomials and Pell–Abel equation, Fundam. Prikl. Mat., 2001, Volume 7, Issue 4, P 1123–1145, gen>

Wegener1981, An application of Pell's equation, Fibonacci Quart. 1981 (19,5): 450-451, fibqy>

Yokota2010, Solutions of polynomial Pell’s equation, J. Number Theory 130 (2010) 2003–2010, jou>

permanents

KaygisizSahin2013b, Determinants and Permanents of Hessenberg matrices and generalized Lucas polynomials, Bull. Iranian Math. Soc. Vol. 39 No. 6 (2013), 1065-1078, nat>

permutations

Atkinson1999, Restricted permutations, Discrete Math. 195 (1999) 27-38, gen>

BabsonSteingrimsson2000, Generalized permutation patterns and a classication of the Mahonian statistics, Sém. Lothar. Combin (2000) Vol. 44, page B44b, 18 p, gen>

BerniniBouvelFerreri2006 (1), Some statistics on permutations avoiding generalized patterns, GASCom 2006, Sep 2006, Dijon, France, gen>

BerniniBouvelFerreri2006 (2), Some statistics on permutations avoiding generalized patterns, arXiv (29 Nov 2006), aXv>

BrandenClaessonSteingrimsson2002, Catalan continued fractions and increasing subsequences in permutations, Discrete Math. 258 (2002), 275–287, gen>

CorteelJosuat-VergčsWilliams2010, The matrix ansatz, orthogonal polynomials, and permutations, arXiv (15 May 2010), aXv>

DokosDwyerJohnsonSaganSelsor2012, Permutation patterns and statistics, Discrete Math. Vol. 312, Issue 18, 28 Sep 2012, 2760–2775, gen>

Egge2007, Restricted colored permutations and Chebyshev polynomials, Discrete Math. Vol. 307, Issue 14, 28 Jun 2007, 1792–1800, gen>

Elizalde2006, Asymptotic enumeration of permutations avoiding generalized patterns, Adv. Appl. Math. 36 (2006), 138–155, gen>

ElizaldeMansour2005, Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials, Discrete Math. 305 (2005) 170–189, gen>

Krattenthaler2001, Permutations with restricted patterns and Dyck paths, Adv. Appl. Math. 27, 510–530 (2001), gen>

Mansour2004c, Restricted 132-Dumont permutations, Australas. J. Combin. Vol. 29 (2004), 103–117, nat>

MansourVainshtein2000, Restricted permutations, contined fractions, and Chebyshev polynomials, Electron. J. Combin. 7 (2000), #R17, gen>

MansourVainshtein2001, Restricted 132-avoiding permutations, Adv. in Appl. Math. 26, 258–269 (2001), gen>

MansourVainshtein2002, Restricted permutations and Chebyshev polynomials, Sém. Lothar. Combin. 47 (2002), Article B47c, gen>

Parviainen2006, Lattice path enumeration of permutations with k occurrences of the pattern 2-13, J. Integer Seq. Vol. 9 (2006), Article 06.3.2, jis>

Rajaraman2012, Asymptotic behaviour of permutations avoiding generalized patterns, MATH 821-Final Projects Dec 2010, Simon Fraser University, gen>

Robertson1999, Permutations containing and avoiding 123 and 132 patterns, arXiv (29 Mar 1999), aXv>

Robertson2004, Restricted permutations from Catalan to Fine and back, Sém. Lothar. Combin 50 (2004), Article B50g, gen>

RobertsonWilfZeilberger1999, Permutation patterns and continued fractions, Electron. J. Combin. 6 (1999), #R38 2, jou>

Perrin

KaygisizSahin2013a, Generalized Van der Laan and Perrin polynomials, and generalizations of Van der Laan and Perrin numbers, Selçuk J. Appl. Math. Vol. 14. No. 1. 89-103, 2013, nat>

Poisson-Charlier

Privault2011, Generalized Bell polynomials and the combinatorics of Poisson central moments, The electr. j. of comb. 18 (2011), gen>

polynomial_mixed-type

KimKim2013c , Higher -order Cauchy of the first kind and poly-Cauchy of the first kind mixed type polynomials , arXix (9 Aug 2013), aXv>

KimKim2013e, Poisson-Charlier and poly-Cauchy mixed-type polynomials, arXix (4 Sep 2013), aXv>

KimKimKwonSeo2014, Identities of some special mixed-type polynomials, Adv. Studies Theor. Phys. Vol. 8, 2014, no. 17, 745  54,

poly-numbers, poly-polynomials

Kamano2012, Sums of products of poly-Bernoulli numbers of negative index, J. Integer Seq. Vol. 15 (2012), Article 12.1.3, aXv>

Kaneko1997, Poly-Bernoulli numbers, J. Théor. Nombres Bordeaux, tome 9, No. 1 (1997), 221-228, nat>

Komatsu2013a, Poly-Cauchy numbers, Kyushu J. Math. 67 (2013), 143–153, nat>

Komatsu2013b, Sums of products of Cauchy numbers, including poly-Cauchy numbers, J. Discrete Math. Vol, 2013 (2013), Article ID 373927, 10 p, jou>

Komatsu2013c, Poly-Cauchy numbers and poly-Bernoulli numbers, xxxx, xxxx>

posets

Bidkhori2011, Finite Eulerian posets which are binomial or Sheffer, FPSAC 2011, Reykjavı'k, Iceland (DMTCS), proc. AO, 2011, 159–170, gen>

Bidkhori2012, Finite Eulerian posets which are binomial, Sheffer or triangular, J. Combin. Theory Ser. A, Vol. 119, Issue 3, Apr 2012, 765–787, jou>

EhrenborgReaddy2006, Characterization of Eulerian binomial and Sheffer posets, Formal Power Series and Algebraic Combinatorics-San Diego, California 2006, gen>

process

Anshelevich2004a, q- Lévy processes, arXiv (21 Jan 2004), aXv>

BrycWesolowski2004, Conditional moments of q-Meixner processes, arXiv (13 Dec 2004), aXv>

DelfertEinzigerRawlings2003, The derangement problem relative to the Mahonian process, Int. J. Math. Math. Sci. Vol. 2003 (2003), Issue 24, 1497-1508, gen>

production matrices

DeutschFerrariRinaldi2005, Production matrices, Adv. Appl. Math. Vol. 34, Issue 1, Jan 2005, 101–122, gen>

q-analogue calculus

AskeyRahmanSuslov1996, On a general q-Fourier transformation with nonsymmetric kernels, J. Comp. Appl. Math. Vol. 68, Issues 1–2, Apr 1996, 25–55, jou>

Berndt2000, Flowers which we cannot yet see growing in Ramanujan’s garden of hypergeometric series, elliptic functions, and q ’s, Nato Sci. Ser. II Math. Phys. Chem. Vol. 30, 2001, 61-85, gen>

Berndt2010, What is a q-series?, Ramanujan Math. Soc. Lect. Notes Ser. Ramanujan Rediscovered, 2010, 31-51, gen>

Cameron2013, Enumerative combinatorics 5: q-analogues, The LTCC lectures- Autumn 2013, gen>

Dhaouadi2013, On the q-Bessel Fourier transform, Bull. Math. Anal. Appl. Vol. 5 Issue 2 (2013), 42-60, nat>

Ernst2008c, The different tongues of q-calculus, Proc. Est. Acad. Sci. 2008, 57, 2, 81–99, nat>

Ernst2009, q-calculus as operational algebra, Proc. Est. Acad. Sci. 2008, 58, 2, 73-97, nat>

Ernst2011, q-analogues of general reduction formulas by Buschman and Srivastava and an important q-operator reminding of Macrobert, Demonstratio Math. Vol. XLIV No 2 2011, gen>

Ernst2013, An umbral approach to find q-analogues of matrix formulas, Linear Algebra Appl. Vol. 439, Issue 4, Aug 2013, 1167–1182, gen>

IsmailRahmanSuslov1997, Some summation theorems and transformations for q-series, Can. J. Math. Vol. 49 (3), 1997, 543–567, nat>

Koornwinder1996, Special functions and q-commuting variables, Special Functions, q-Series and Related Topics, 131–166 , aXv>

Koornwinder2005a, q-special functions, an overview, arXiv (6 Nov 2005), aXv>

Koornwinder2013, q-special functions, a tutorial, arXiv (14 Oct 2013), aXv>

Koornwinder2014, Additions to the formula lists in "Hypergeometric orthogonal polynomials and their q-analogues" by Koekoek, Lesky and Swarttouw, arXiv (4 Jan 2014), aXv>

KoornwinderSwarttouw1992, On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. Vol. 333, No. 1, Sep 1992, nat>

MelhamShannon1995a, Some summation identities using generalized Q-matrices, Fibonacci Quart. 1995 (33,1): 64-73, fibqy>

PurohitKalla2007, On q-Laplace transforms of the q-Bessel functions, Fract. Calc. Appl. Anal. Vol. 10, No. 2, (2007), 189-196, gen>

Yang1988, Limits of q-polynomial coeficients, Fibonacci Quart. 1988 (26,1): 64-69, fibqy>

Racah coefficients

ArimaHorieTanabe1954, Generalized Racah coefficient and its applications, Progr. Theoret. Phys. Vol. 11, No.2, Feb 1954, gen>

EliasGingold2010, Approximation of the Jacobi polynomials and the Racah coefficients, Rocky Mountain J. Math. Vol. 40, No. 3, 2010, nat>

Groenevelt2005, Wilson function transforms related to Racah coefficients, arXiv (28 Jan 2005), aXv>

recurrence relations

AgohDilcher2009, Higher-order recurrences for Bernoulli numbers, J. Number Theory 129, Issue 8, Aug 2009, 1837–1847, jou>

Aloui2015, Hankel Determinant for a Sequence that Satisfies a Three-Term Recurrence Relation, J. Integer Seq. Vol. 18 (2015), Article 15.1.5,  jis>

Ando1995, On a system of sequences defined by a recurrence relation, Fibonacci Quart. 1995 (33,3): 279-282,  fibqy>

AndradePethe1992, On the rth-order nonhomogeneous recurrence relation and some generalized Fibonacci sequences, Fibonacci Quart. 1992 (30,3): 256-262, fibqy>

André-Jeannin1997, Summation of reciprocals in certain second-order recurring sequences, Fibonacci Quart. 1997 (35,1): 68-74, fibqy>

AskeyWilson1984, A recurrence relation generalizing those of Apéry, J. Aust. Math. Soc. Vol. 36 / Issue 02 / Apr 1984, 267-278, nat>

AtanassovHleBarskaMihov1992, Recurrent formulas of the generalized Fibonacci and Tribonacci sequences, Fibonacci Quart. 1992 (30,1): 77-79, fibqy>

BarberoSalasVillasenior2013, Bivariate generating functions for a class of linear recurrences. II. Applications, arXiv (22 jul 2013), aXv>

BarnabeiBriniNicoletti1982, Recursive matrices and umbral calculus, J. Algebra Vol. 75, Issue 2, Apr 1982, 546–573, jou>

Barry2009c, Symmetric third-order recurring sequences, Chebyshev polynomials, and Riordan arrays, J. Integer Seq. Vol. 12 (2009), Article 09.8.6, jis>

BarryHennessy2012a, Four-term recurrences, orthogonal polynomials and Riordan arrays, J. Integer Seq., Vol. 15 (2012), Article 12.4.2, jis>

BelbachirKomatsuSzalay2014, Linear recurrences associated to rays in Pascal's triangle and combinatorial identities, Math. Slovaca 64 (2014), No. 2, 287–300, nat>

BenderDaalhuisGaoRichmondWormald2010, Asymptotics of some convolutional recurrences, Electron. J. Combin. 17 (2010), gen>

BenjaminDerksQuinn2011, The combinatorialization of linear recurrences, Electron. J. Combin. 18 (2) (2011), gen>

BerezanskyIvasiukMokhonko2008, Recursion relation for orthogonal polynomials on the complex plane, Methods Funct. Anal. Topology Vol. 14 (2008), no. 2, 108–116, gen>

BergumHoggatt, Jr.1975, Sums and products for recurring sequences, Fibonacci Quart. 1976 (14,2): 115-120, fibqy>

BirmajerGilWeiner2015, Linear recurrence sequences and their convolutions via Bell polynomials, J. Integer Seq. Vol. 18 (2015), Article 15.1.2, jis>

Brousseau1976, Recursion relations of products of linear recursion sequences, Fibonacci Quart. 1976 (14,2): 159-166, fibqy>

Callan2005, A combinatorial interpretation for a super-Catalan recurrence, J. Integer Seq. Vol. 8 (2005), Article 05.1.8, jis>

CarlipSomer2003, The existence of special multipliers of second-order recurrence sequences, Fibonacci Quart. 2003 (41,2): 156-168, fibqy>

Cheon G-S.HwangRimSong2003, Matrices determined by a linear recurrence relation among entries, Linear Algebra Appl Vol. 373, Nov 2003, 89–99, gen>

ChenShapiro2007, On sequences Gn satisfying Gn = (d + 2)Gn−1 − Gn−2, J. Integer Seq. Vol. 10 (2007), Article 07.8.1, jis>

CookBacon2013, Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations, Ann. Math. Inform. 41 (2013), 27–39, gen>

CorvajaZannier2002, Finiteness of integral values for the ratio of two linear recurrences, Invent. Math. (2002) Aug. 2002, Vol. 149, Issue 2, 431-451, gen>

Djordjevic2005a, Some properties of the sequences C_(n,3)=C_(n-1,3)+C_(n-3,3)+r, Fibonacci Quart. 2005 (43,3): 202-207, fibqy>

DombrowskiNevai1986, Orthogonal polynomials, measures and recurrence relations, SIAM J. Math. Anal. 1986, Vol. 17, No. 3 : 752-759, gen>

DukeGreenfieldSpeer1998, Properties of a quadratic Fibonacci recurrence, J. Integer Seq. Vol. 1 (1998), Article 98.1.8, jis>

Everest van der PoortenShparlinskiWard2003, Recurrence sequences, Mathematical Surveys and Monographs, vol 104, gen>

Ford1967, A shift formula for recurrence relations of order m, Fibonacci Quart. 1967 (5,5): 461-465, fibqy>

Frenklach1985, Linear recurrence relations with binomial coefficients, Fibonacci Quart. 1985 (23,4): 359-363, fibqy>

Gerhold2009, The shape of the value sets of linear recurrence sequences, J. Integer Seq. Vol. 12 (2009), Article 09.3.6, jis>

Gould1963, Operational recurrences involving Fibonacci numbers, Fibonacci Quart. 1963 (1,1): 30-33, fibqy>

Gould1975, Formal proof of equivalence of two solutions of the general Pascal recurrence, Fibonacci Quart. 1975 (13,2): 127-128, fibqy>

HamzaAhmedYoussef2011, On the recursive sequence x(n+1)=(a+ţx(n))/A+Bx(^k)(n-1), Arab J. Math. Sci. Vol. 17, Issue 1, Jan 2011, 31–44, nat>

HeShiue2009, On sequences of numbers and polynomials defined by linear recurrence relations of order 2, Int. J. Math. Math. Sci. Vol. 2009 (2009), Article ID 709386, 21 p, gen>

Horadam1992b, Generation of Genocchi polynomials of first order by recurrence relations, Fibonacci Quart. 1992 (30,3): 239-242, fibqy>

Howard1994, Congruences and recurrences for Bernoulli numbers of higher order, Fibonacci Quart. 1994 (32,4): 316-328, fibqy>

Howard1995, Applications of a recurrence for the Bernoulli numbers, J. Number Theory, Vol. 52, Issue 1, May 1995, 157–172, jou>

HuSun Z-W.Liu2001, Reciprocal sums of second-order recurrent sequences, Fibonacci Quart. 39(2001), no. 3, 214–220, fibqy>

Janjic2012, Determinants and recurrence sequences, J. Integer Seq. Vol. 15 (2012), Article 12.3.5, jis>

Katriel2008, On a generalized recurrence for Bell numbers, J. Integer Seq. Vol. 11 (2008), Article 08.3.8, jis>

KiliçStanica2011, A matrix approach for general higher order linear recurrences, Bull. Malays. Math. Sci. Soc. (2) 34(1) (2011), 51–67, nat>

KitaevMansour2005, Linear recurrences and Chebyshev polynomials, Fibonacci Quart. 2005 (43,3): 256-261, fibqy>,

Labelle1980, Sur l'inversion et l'itération continue des séries formelles, European J. Combin. Vol. 1, Issue 2, Jun 1980, 113–138, gen>

Lee G-Y.KimSho2003, Generalized Fibonacci functions and sequences of generalized Fibonacci functions, Fibonacci Quart. 2003 (41,2): 108-121, fibqy>

Lee1997, On some basic properties of the second-order inhomogeneous line-sequence, Fibonacci Quart. 1997 (35,2): 111-121, fibqy>

Lehmer1935, Lacunary recurrence formulas for the numbers of Bernoulli and Euler, Ann. of Math. (2), Vol. 36, No. 3, (Jul 1935), 637-649, nat>

LenstraShallit1992, Continued fractions and linear recurrences, Math. Comp. 61, No. 203, Jul 1993, 351-354, gen>

Levesque1985, On m-th order linear recurrences, Fibonacci Quart. 1985 (23,4): 290-293, fibqy>

Lewanowicz1996, Recurrence relations for the connection coefficients orthogonal polynomials of a discrete variable, J. Comput. Appl. Math. Vol. 76, Issues 1–2, 17 Dec 1996, 213–229, gen>

Liu1992, A matrix method to solve linear recurrences with constant coefficients, Fibonacci Quart. 1992 (30,1): 2-8, fibqy>

LiuQiDing2010 , Some recurrence relations for Cauchy numbers of the first kind , J. Integer Seq. Vol. 13 (2010), Article 10.3.8 fibqy>

LuzonMoron2010, Recurrence relations for polynomial sequences via Riordan matrices, Linear Algebra Appl. Vol. 433, Issue 7, Dec 2010, 1422–1446, gen>

Mansour2006, Combinatorial methods and recurrence relations with two indices, J. Difference Equ. Appl. Vol. 12, Issue 6, 2006, jou>

MansourShattuck2013a, A combinatorial approach to a general two-term recurrence, Discrete Appl. Math. Vol. 161, Issues 13–14, Sep 2013, 2084–2094, gen>

MelhamJennings1995, On the general linear recurrence relation, Fibonacci Quart. 1995 (33,2): 142-146, fibqy>

MihoubiBelbachir2014, Linear recurrences for r-Bell polynomials, J. Integer Seq. Vol. 17 (2014), Article 14.10.6, jis>

Mills1975, Continued Fractions and Linear Recurrences, Math. Comp. Vol. 29, No 129, Jan 1975, 173-180, gen>

Momiyama2001, A new recurrence formula for Bernoulli numbers, Fibonacci Quart. 2001 (39,3): 285-288, fibqy>

Neuwirth2001, Recursively defined combinatorial functions: extending Galton’s board, Discrete Math. Vol. 239, Issues 1–3, Aug 2001, 33–51, gen>

Nevai1979, Orthogonal polynomials defined by a recurrence relation, Trans. Amer. Math. Soc. Vol. 250 (Jun 1979), 369-384, nat>

Rabinowitz1999b, Algorithmic manipulations of second-order linear recurrences, Fibonacci Quart. 1999 (37,2): 162-176, fibqy>

Robbins1982, Some identities and divisibility properties of linear second-order recursion sequences, Fibonacci Quart. 1982 (20,1): 21-23, fibqy>

RonveauxZarzoGodoy1995, Recurrence relations for connection coefficients between two families of orthogonal polynomials, J. Comp. Appl. Math. Vol. 62, Issue 1, Aug 1995, 67-73, jou>

Rota1964, The number of partitions of a set, Amer. Math. Monthly, Vol. 71, No 5 (May, 1964), 498-504, nat>

Sburlati2007, Generalized Fibonacci sequences and linear recurrences, Rend. Sem. Mat. Univ. Pol. Torino - Vol. 65, 3 (2007), nat>

Shannon1974a, Explicit expressions for powers of linear recursive sequences, Fibonacci Quart. 1974 (12,3): 281-287, fibqy>

Shannon1974c, Some properties of a fundamental recursive sequence of arbitrary order, Fibonacci Quart. 1974 (12,4): 327-334, fibqy>

ShannonOllerton2002, Combinatorial matrices and linear recursive sequences, Fibonacci Quart. 2002 (40,5): 417-423, fibqy>

Shi1995, Concerning the recursive sequences An+k = Σi=1 kaiAain+i-1 , Fibonacci Quart. 1995 (33,3): 240-243, fibqy>

ShoreyStewart1987, Pure powers in recurrent sequences and some related Diophantine equations, J. Number Theory Vol, 27, Issue 3, Nov 1987, 324–352, jou>

Spilker1997, Initial values for homogeneous linear recurrences of second order, Fibonacci Quart. 1997 (35,1): 24-27, fibqy>

Spivey2011, On solutions to a general combinatorial recurrence, J. Integer Seq. Vol. 14 (2011), Article 11.9.7, jis>

Stanica2005, Cholesky factorizations of matrices associated with r-order recurrent sequences, Integers 5(2) (2005), gen>

Steffensen1928, A general summation formula, Det Kgl . Danske Videnskabernes Selskab . Mathematisk-fysiske Meddelelser . VIII, 7 , gen>

Strehl1992, Recurrences and Legendre Transform, Sém. Lothar. Combin. B29b (1992), 22 p. 29 Thurnau, Sep 1992, gen>

Sun Z-H.2001b, Linear recursive sequences and powers of matrices, Fibonacci Quart. 2001 (39,4): 339-351, fibqy>

Sury2009, Generalized Catalan numbers: linear recursion and divisibility, J. Integer Seq. Vol. 12 (2009), Article 09.7.5, jis>

TianmingZhizheng1996, Recurrence sequences and Nörlund-Euler polynomials, Fibonacci Quart. 1996 (34,4): 314-319, fibqy>

WimpZeilbercer1985, Resurrecting the asymptotics of linear recurrences, J. Math. Anal. Appl. 111, 162-176 (1985), jou>

Yang S-l.2012, Recurrence relations for the Sheffer sequences, Linear Algebra Appl. Vol. 437, Issue 12, Dec 2012, 2986–2996, gen>

Zannier2005, Diophantine equations with linear recurrences An overview of some recent progress, J. Théor. Nombres Bordeaux 17 (2005), 423–435, nat>

ZekiriBencherif2011, A new recursion relationship for Bernoulli numbers, Ann. Math. Inform. 38 (2011), 123–126, gen>

Zhang Z.1997a, Some properties of the generalized Fibonacci sequences C(n) = C(n-1)+ C(n-2) + r, Fibonacci Quart. 1997 (35,2): 169-171, fibqy>

Zhang Z.1998, Recurrence sequences and Nordlund-Bernoulli polynomials, Math. Morav. Vol. 2 (1998), 161-168, nat>

Zhang Z.Wang X.2002, A note on a class of computational formulas involving the multiple sum of recurrence sequences, Fibonacci Quart. 2002 (40,5): 394-397, fibqy>

Zollner1993, A disjoint system of linear recurring sequences generated by u(n+2) = u(n+1) + u(n) which contains every natural number, Fibonacci Quart. 1993 (31,2): 162-164, fibqy>

renewal array, process

Rogers1978, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math. Vol. 22, Issue 3, 1978, 301–310, gen>

Weiss1962, Laguerre expansions for successive generations of a Renewal Process, J. Research National Bureau of Standards-B. Math. and Math. Physics, Vol. 66B, No.4, Oct- Dec 1962, jou>

Riemann (see also z-function)

AraciBagdasaryanOzelSrivastava2014, New symmetric identities involving q-zeta type functions, Appl. Math. Inf. Sci. 8, No. 6, 2803-2808 (2014),  

ByrnesJiuMollVignat2013, Recursion rules for the hypergeometric zeta function, arXiv (8 May 2013),

CandelpergherCoppo2012, A new class of identities involving Cauchy numbers, harmonic numbers and zeta values, Ramanujan J. April 2012, Volume 27, Issue 3, 305-328,

Chu1997a, Hypergeometric series and the Riemann zeta function, Acta Arith. LXXXII.2 (1997),

HassenNguyen2005, Hypergeometric zeta functions, arXiv (27 Sep 2005), aXv>

IbrahimDarus2011, On operator defined by double zeta functions, Tamkang J. Math. Vol. 42, No. 2, 163-174, Summer 2011,

Ivic2008, The Laplace and Mellin transforms of powers of the Riemann zeta-function, arXiv (2 Jun 2006),

Kim2006b, q-analogue of Euler- Barnes multiple zeta functions, arXiv (6 Mar 2006),

Kim2009a, q-Euler numbers and polynonials associated with multiple q-zeta functions, arXiv (24 Dec 2009),  

Kim2009b, Barnes type multiple q-zeta functions and q-Euler polynomials, arXiv (28 Dec 2009),

KimRimSimsekKim2008, On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions, J. Korean Math. 45 (2008), No. 2, 435-453,

KimRyooJangRim2005, Exploring the q-Riemann zeta function and q-Bernoulli polynomials, Discrete Dyn. Nat. Soc. Vol. 2005 (2005), Issue 2, 171-181,

KimSimsek2005, Barnes’ type multiple Changhee q-zeta functions, arXiv (10 Fev 2005),

KimSimsekSrivastava2005, q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, arXiv (1 Fev 2005),  

Laurincikas2010, Universality of the Riemann zeta-function, J. Number Theory Vol. 130, Issue 10, Oct 2010, 2323–2331,

Soria-LorenteCumbrera-Gonzales2014, q-hypergeometric representations of the q-analogue of zeta function, J. of Fractional Calculus and Applications Vol. 5 (2) Jul 2014, 1-8,  

Soundrarajan2009, Moments of the Riemann z-function, Ann. of Math. (2), 170 (2009), 981–993,

Sury2003, Bernoulli numbers and the Riemann zeta function, Resonance Jul 2003, Vol. 8, Issue 7, 54-62,  

Riordan arrays

AgapitoMestrePetrulloTorres2011, Riordan arrays and applications via the classical Umbral Calculus, arXiv (30 Mar 2011), aXv>

AgapitoMestrePetrulloTorres2013, A symbolic treatment of Riordan arrays, Linear Algebra App. Vol. 439, Issue 7, Oct 2013, 1700–1715, gen>

Barry2009c, Symmetric third-order recurring sequences, Chebyshev polynomials, and Riordan arrays, J. Integer Seq. Vol. 12 (2009), Article 09.8.6, jis>

Barry2010b, The restricted Toda chain, exponential Riordan arrays, and Hankel transforms, J. Integer Seq. Vol. 13 (2010), Article 10.8.4, jis>

Barry2011a, Riordan arrays, orthogonal polynomials as moments, and Hankel transforms, J. Integer Seq. Vol. 14 (2011), Article 11.2.2, jis>

Barry2011c, Combinatorial polynomials as moments, Hankel transforms, and exponential Riordan arrays, J. Integer Seq. Vol. 14 (2011), Article 11.6.7, jis>

Barry2011d, Eulerian polynomials as moments, via exponential Riordan arrays, J. Integer Seq. Vol. 14 (2011), Article 11.9.5, jis>

Barry2013e, General Eulerian polynomials as moments using exponential Riordan arrays, J. Integer Seq. Vol. 16 (2013), Article 13.9.6, jis>

Barry2013f, Laurent biorthogonal polynomials and Riordan arrays, arXiv (10 Nov 2013), aXv>

Barry2013g, Comparing two matrices of generalized moments defined by continued fraction expansions, arXiv (27 Nov 2013), aXv>

Barry2014a, Generalized Stirling numbers, exponential Riordan arrays, and Toda chain equations, J. Integer Seq. Vol. 17 (2014), Article 14.2.3, jis>

Barry2014c, Embedding structures associated with Riordan arrays and moment matrices, Int. J. Comb. Vol. 2014 (2014), Article ID 301394, 7 p, gen>

BarryHennessy2012a, Four-term recurrences, orthogonal polynomials and Riordan arrays, J. Integer Seq., Vol. 15 (2012), Article 12.4.2,  jis>

BarryHennessy2012b, Riordan arrays and the LDU decomposition of symmetric Toeplitz plus Hankel matrices, Linear Algebra Appl. Vol. 437, Issue 6, Sep 2012, 1380–1393, gen>

BalofMenashe2007, Semiorders and Riordan Numbers, J. Integer Seq. Vol. 10 (2007), Article 07.7.6, jis>

BelbachirKomatsuSzalay2014, Linear recurrences associated to rays in Pascal's triangle and combinatorial identities, Math. Slovaca 64 (2014), No. 2, 287–300, nat>

Cheon G-S.El-Mikkawy2008, Generalized harmonic numbers with Riordan arrays, J. Number Theory Vol. 128, Issue 2, Feb 2008, 413–425, jou>

Della Riccia2008, Riordan arrays, Sheffer sequences and “Orthogonal” Polynomials, J. Integer Seq. Vol. 11 (2008), Article 08.5.3,  jis>

Egorychev(2011), Combinatorial sums: Egorychev’s method of coefficients and     Riordan arrays, J. Kepler Universitat Linz, Technisch-Naturwissenschaftliche Fakult¨at (Linz,  2011), thesis

He2011a, Riordan arrays associated with Laurent series and generalized Sheffer-type groups, Linear Algebra Appl. Vol. 435, Issue 6, Sep. 2011, 1241–1256, gen>

He2017, Riordan Arrays and Double Riordan Arrays, 2017 Internat. Conf. on Combinatorics Inst. of Math., Academia Sinica, Taipei, Ta (May 19 – 22, 2017), gen>

Nkwanta2008, Lattice Paths, Riordan Matrices and RNA Numbers, Congr. Numer. 01/2008, gen>

Nkwanta2003, A Riordan matrix approach to unifying a selected class of combinatorial arrays, Congr. Numer. 160 (2003), 33-45, gen>

Nkwanta2010, Riordan matrices and higher-dimensional lattice walks, J. of Statist. Plann. Inference Vol. 140, Issue 8, Aug 2010, 2321–2334, jou>

NkwantaBarnes2012, Two Catalan-type Riordan arrays and their connections to the Chebyshev polynomials of  the first kind, J. Integer Seq. Vol. 15 (2012), Article 12.3.3, jis>

NkwantaKnox1999, A note on Riordan matrices, Thesis-Contemp. Math. Vol. 252. 1999, Howard University, Washington, DC 1997, gen>

NkwantaShapiro2005, Pell walks and Riordan matrices, Fibonacci Quart. 2005 (43,2): 170-180, fibqy>
Sprugnoli1994, Riordan arrays and combinatorial sums, Discrete Math. Vol. 132, Issues 1–3, Sep 1994, 267-290, gen>

Riordan group, (q-analogue) (see also Sheffer group)

Agapito2010, A classical umbral view of the Riordan group and related Sheffer sequences, Algebra and Combinatorics Seminar, Nov 26, 2010, gen>

Cameron2011, Combinatorics with the Riordan Group, NUMS Conference Reed College, Apr 9, 2011,  gen>

CameronNkwanta2005, On some (pseudo) involutions in the Riordan group, J. Integer Seq. Vol. 8 (2005), Article 05.3.7,  jis>

Cheon G-S.KimShapiro2008, Riordan group involutions, Linear Algebra Appl. Vol. 428, Issue 4, Feb 2008, 941–952, gen>

CheonJinKimShapiro2009, Riordan group involutions and the Δ-sequence, Discrete Appl. Math. 157 (2009) 1696-1701,  gen>

CheonKim2008, Simple proofs of open problems about the structure of involutions in the Riordan group, Linear Algebra Appl. Vol. 428, Issue 4, Feb 2008, 930–940, gen>

CheonYungLim2013, A q-analogue of the Riordan group, Linear Algebra Appl Vol. 439, Issue 12, Dec 2013, 4119–4129,  gen>

He2011a, Riordan arrays associated with Laurent series and generalized Sheffer-type groups, Linear Algebra Appl. Vol. 435, Issue 6, Sep. 2011, 1241–1256, gen>

He2017, Riordan Arrays and Double Riordan Arrays, 2017 Internat. Conf. on Combinatorics Inst. of Math., Academia Sinica, Taipei, Ta (May 19 – 22, 2017), gen>

HeHsuShiue2007, The Sheffer group and the Riordan group, Discrete Applied Math. Vol. 155, Issue 15, 15 Sep 2007, 1895–1909, gen>

Jean-LouisNkwanta2013, Some algebraic structure of the Riordan group, Linear Algebra Appl. Vol. 438, Issue 5, Mar 2013, 2018–2035, gen>

LuzonMoron2008, Ultrametrics, Banach’s fixed point theorem and the Riordan group, Discrete Appl. Math.. Vol. 156, Issue 14, Jul 2008, 2620–2635, gen>

PeartWoan2000b, A divisibility property for a subgroup of Riordan matrices, Discrete Appl. Math. Vol. 98, Issue 3, Jan 2000, 255–263, gen>

PoinsotDuchamp2010, A formal calculus on the Riordan near algebra, Adv. Appl. Discrete Math. 2010, 6 (1), 11-44, gen>

Shapiro2003, Bijections and the Riordan group, Theoret. Comput. Sci. Vol. 307, Issue 2, 7 Oct 2003, 403–413,  gen>

ShapiroGetuWoanWoodson1991, The Riordan group, Discrete Appl. Math. Vol. 34, Issues 1–3, 21 Nov 1991, 229–239, gen>

RNA secondary structures, numbers

 EllingtonWachiraNkwanta2010, RNA secondary structure prediction by using discrete math.: An interdisciplinary research experience for undergraduate students, CBE—Life Sciences Education Vol. 9, 348–356, Fall 2010, gen>

Nkwanta2008, Lattice Paths, Riordan Matrices and RNA Numbers, Congr. Numer. 01/2008, gen>

Nkwanta2009, Lattice path and RNA secondary structure predictions, Fifteenth Conf. for Afri. Amer. Researchers in the Math. Sci-Rice University, June 23-26, 2009 , gen>

Rodrighes

AgrawalChaubey1981, Bilateral generating relations for a function defined by generalized Rodrigues formula, Indian J. Pure Appl. Math. 12(3): 377-379, Mar 1981,  nat>

Horadam1997b, Rodriques' formulas for Jacobsthal-type polynomials, Fibonacci Quart. 1997 (35,4): 361-370, fibqy>

PatilThakare1977, Bilateral generating function for a function defined by generalized Rodrigue's formula, Indian J. Pure Appl. Math. 1977 (8,4): 425-429,  nat>

Radulescu2008, Rodrigues-type formulae for Hermite and Laguerre polynomials, An. S¸t. Univ. Ovidius Constant¸a Vol. 16 (2), 2008, 109–116,  nat>

Robin2012, On the Rodrigues’ formula approach to operator factorization, Int. Mathematical Forum, Vol. 7, 2012, no. 47, 2333 - 2351, gen>

SrivastavaSingh1979b, Some generating relations connected with a function defined by a generalized Rodrigues formula, Indian J. Pure Appl. Math. 10 (10): 1312-1317, Oct 1979, nat>

Salié

PanSun Z-W.2006b, On q-Euler numbers, q-Salié numbers and q-Carlitz numbers, Acta Arith. 124 (2006), no. 1, 41–57, gen>

Schröder

BrualdiKirkland2005, Aztec diamonds and digraphs, and Hankel determinants of Schröder numbers, J. Combin. Theory Ser. B, 94 (2005), 334–351, jou>

DengYan2008, Some identities on the Catalan, Motzkin and Schröder numbers, Discrete Appl. Math. Vol. 156, Issue 14, Jul 2008, 2781–2789, gen>

EuWongYeh2012, Hankel determinants of sums of consecutive weighted Schröder numbers, Linear Algebra Appl. Vol. 437, Issue 9, 1 Nov 2012, 2285–2299, gen>

Muntingh2012, Implicit divided differences, little Schröder numbers, and Catalan numbers, J. Integer Seq. Vol. 15 (2012), Article 12.6.5, jis>

Schröder2007, Generalized Schröder numbers and the rotation principle, J. Integer Seq. Vol. 10 (2007), Article 07.7.7, jis>

Sun Z-W.2011a, On Delannoy numbers and Schröder numbers, J. Number Theory, Vol. 131, Issue 12, Dec 2011, 2387–2397, jou>

Yang S-l.ZhengYuanHe2013, Schröder matrix as inverse of Delannoy matrix, Linear Algebra Appl. Vol. 439, Issue 11, Dec 2013, 3605–3614, gen>

Schubert

Fulton1999, Universal Schubert polynomials, Duke Mathematical J. 1999, Vol. 96, No. 3, 575-594, gen>

Kirillov2004, Cauchy identities for universal Schubert polynomials, J. Math. Sci. May 2004, Vol. 121, Issue 3, 2360-2370, aXv>

Schur

Grandati2013, Exceptional orthogonal polynomials and generalized Schur polynomials, arXiv (18 Nov 2013), aXv>

Lenart2000, Lagrange Inversion and Schur functions, J. Algebraic Combin. 11 (2000), 69–78, jou>

Seidel-Arnold

Dumont1995, Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers, Adv. Appl. Math. Vol. 16, Issue 1, 1995, 275-296,  gen>

Sheffer group (see also Riordan group, (q-analogue)) HeHsuShiue2007, The Sheffer group and the Riordan group, Discrete AppliedMath Vol. 155, Issue 15, 15 Sep 2007, 1895–1909, gen>

Sheffer polynomial sequences

Agapito2010, A classical umbral view of the Riordan group and related Sheffer sequences, Algebra and Combinatorics Seminar, Nov 26, 2010, gen>

BrownRoman1981, Inverse relations for certain Sheffer sequences, Siam J. Math. Anal. Vol.12, No. 2, Mar 1981, gen>

Campos-OrozcoGalé2013, Continuous Sheffer families I, J. Math. Anal. Appl. Vol. 405, Issue 1, 1 Sep 2013, 286–296, jou>

Campos-OrozcoGalé2014, Continuous Sheffer families II, J. Math. Anal. Appl.Vol. 412, Issue 1, 1 Apr 2014, 381–390, jou>

CostabileLongo2014, An algebraic approach to Sheffer polynomial sequences, Integral Transforms Spec. Funct. Vol. 25, Issue 4, 2014, gen>

Della Riccia2008, Riordan arrays, Sheffer sequences and “Orthogonal” Polynomials, J. Integer Seq. Vol. 11 (2008), Article 08.5.3, jis>

Di NardoNiederhausenSenato2009, The classical umbral calculus: Sheffer sequences, Lect. Notes Semin. Interdiscip. Mat. Vol. 8 (2009), 101–130, gen>

Di NardoNiederhausenSenato2011, A symbolic handling of Sheffer polynomials, Ann. Mat. Pura Appl. (4), Sep. 2011, Vol. 190, Issue 3, 489-506, gen>

KimKim2013d, Some identities arising from Sheffer sequences for the powers of Sheffer pairs under umbral calculus, arXiv (29 Mar 2013), aXv>

KimKimLee2013b, Some identities arising from Sheffer sequences for the powers of Sheffer pairs under umbral composition, Appl. Math. Sci. (Ruse) Vol. 7, 2013, no. 106, 5287-5299, gen>

KimKimLeeDolgy2014, Some special polynomials and Sheffer sequences, J. Comput. Anal. Appl. Jan 2014, Vol. 16, Issue 1, 702-712, jou>

KimKimMansourRimSchork2013, Umbral calculus and Sheffer sequences of polynomials, J. Math. Phys. 54, 083504 (2013), jou>

KimKimRimDolgy2013a, Sheffer sequences of polynomials and their applications, Adv. Difference Equ. 2013, 2013: 118, gen>

NakamuraZhedanov2004, Toda Chain, Sheffer class of orthogonal polynomials and combinatorial numbers, Proc. of Institute of Math. of NAS of Ukraine 2004, Vol. 50, Part 1, 450–457, nat>

Randrianarivony1998, Moments des polynômes orthogonaux unitaires de Sheffer généralisés et spécialisations, European J. Combin. Vol. 19, Issue 4, May 1998, 507–518, gen>

Wang W.Wang T.2009, Identities on Bell polynomials and Sheffer sequences, Discrete Math. Vol. 309, Issue 6, 6 Apr 2009, 1637–1648, gen>

Sheffer-type

He2006, The generalized Stirling numbers, Sheffer-type polynomials and expansion theorems, CBMS/NSF Regional Research Conference, Kent, Aug 2006, gen>

He2011a, Riordan arrays associated with Laurent series and generalized Sheffer-type groups, Linear Algebra Appl. Vol. 435, Issue 6, Sep. 2011, 1241–1256, gen>

He2011b, Characterizations of orthogonal generalized Gegenbauer-Humbert polynomials and orthogonal Sheffer-type polynomials, J. Comput. Anal. Appl. 13.4 (2011): 701-723, jou>

He2012b, The characterization of Riordan arrays and Sheffer-type polynomial sequences, J. Combin. Math. Combin. Comput. 82 (2012): 249-268, jou>

Meredith2003, On polynomials of Sheffer type arising from a Cauchy problem, Int. J. Math. Math. Sci. Vol. 2003 (2003), Issue 33, 2119-2137, gen>

Sobolev

MarcellanXu2015, On Sobolev orthogonal polynomials, Expo. Math. Vol. 33, Issue 3, 2015, 308-352, gen>

MeijerPimar2003, A generating function for Laguerre–Sobolev orthogonal polynomials, J. Approx. Theory Vol. 120, Issue 1, Jan 2003, 111–123, jou>

MorenoGarcia-Caballero2011a, q-Sobolev orthogonality of the q-Laguerre polynomials Ln^(-N) ( ; q)n =0^ for positive integers N, J. Korean Math. Soc. 48 (2011), No. 5, 913-926, nat>

PérezPinar1996, On Sobolev orthogonality for the generalized Laguerre polynomials, J. Approx. Theory Vol. 86, Issue 3, Sep 1996, 278–285, jou>

Springer

Dumont1995, Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers, Adv. Appl. Math. Vol. 16, Issue 1, 1995, 275-296, gen>

Srivastava

KarandePatil1981, Expansion formulas for Srivastava polynomials in series of the Konhauser biorthogonal polynomials, Indian J. Pure Appl. Math. 12(9):124-1128, Sep 1981, nat>

SrivastavaGargChoudhary2010, A new generation of Bernoulli and related polynomials, Russ. J. Math. Phys. Mar Jun 2010, Vol. 17, Issue 2, 251-261, nat>

Srivastava-Pintér addition theorems

Mahmudov2012b, q-analogues of the Bernoulli and Genocchi polynomials and the Srivastava-Pintér addition theorems, Discrete Dyn. Nat. Soc. Vol. 2012 (2012), Article ID 169348, 8 p, gen>

Stern-Brocot sequence

AlloucheMendčs-France2013, Lacunary formal power series and the Stern-Brocot sequence, Acta Arith. Vol. 159, No. 1, (2013), 47-61, aXv>

Stieltjes

PeartWoan2000a, Generating functions via Hankel and Stieltjes matrices, J. Integer Seq. Vol. 3 (2000), Article 00.2.1, jis>

Stirling

AgohDilcher2008, Generalized convolution identities for Stirling numbers of the second kind, Integers 8 (2008), gen>

AgohDilcher2015, Representations of Stirling numbers of the first kind by multiple integrals, Integers 15 (2015), gen>

Barry2014a, Generalized Stirling numbers, exponential Riordan arrays, and Toda chain equations, J. Integer Seq. Vol. 17 (2014), Article 14.2.3, jis>

BelbachirBelkhirBousbaa2014, Combinatorial approach of certain generalized Stirling numbers, arXiv (23 Nov 2014), aXv>

Bickel2003, The group of generalized Stirling numbers, Adv. in Appl. Math. Vol. 26, Issue 1, Jan. 2001, 1–22, gen>

Branson1996, An extension of Stirling numbers, Fibonacci Quart. 1996 (34,3): 213-223, fibqy>

CakicEl-DesoukyMilovanovic2013, Explicit formulas and combinatorial identities for generalized Stirling numbers, Mediterr. J. Math. Feb 2013, Vol. 10, Issue 1, 57-72, nat>

CakicMilovanovic2004, On generalized Stirling numbers and polynomials, Math. Balkanica (N.S.) Vol. 18, 2004, Fasc. 3-4, nat>

CanDagli2014, Extended Bernoulli and Stirling matrices and related combinatorial identities, Linear Algebra Appl. Vol. 444, Mar 2014, 114-131 arXiv(4 Dec 2013), aXv>

Carlitz1978a, Generalized Stirling and related numbers, Rivista di Matematica della Universitŕ di Parma. Serie IV 01/1978; 4.,  nat>

ChanManna2010, Congruences for Stirling numbers of the second kind, Contemporary Math.-Gems in Experimental Math. Vol. 517, 97-11, gen>

Chapman2008, Lagrange inversion and Stirling number convolutions, Integers 8 (2008), gen>

Cheon G-S.Kim2001, Stirling matrix via Pascal matrix, Linear Algebra Appl. Vol. 329, Issues 1–3, May 2001, 49–59, gen>

Cheon G-S.Kim2002, Factorial Stirling matrix and related combinatorial sequences, Linear Algebra Appl. Vol. 357, Issues 1–3, Dec 2002, 247–258, gen>

Corcino R.B.Barrientos2011, Some theorems on the q-analogue of the generalized Stirling numbers, Bull. Malays. Math. Sci. Soc. (2) 34(3) (2011), 487–501, nat>

Davis2013, p-adic Stirling numbers of the second-kind, arXiv (29 Jul 2013), aXv>

Ehrenborg2003, Determinants involving q-Stirling numbers, Adv. Appl. Math. Vol. 31, Issue 4, Nov. 2003, 630–642, gen>

El-Desouky1994, The multiparameter noncentral Stirling numbers, Fibonacci Quart. 1994 (32,3): 218-225, fibqy>

GuoQi2015b, An explicit formula for Bernoulli numbers in terms of Stirling numbers of the second kind, J. Anal. Number Theory, 3, No. 1, 27-30 (2015), jou>

He2011c, Generalized Stirling numbers and generalized Stirling functions, arXiv (26 Jun 2011), aXv>

Hsu1993, A summation rule using Stirling numbers of the second kind, Fibonacci Quart. 1993 (31,3): 256-262, fibqy>

KangRyoo2013, A research on a certain family of numbers and polynomials related to Stirling numbers, central factorial numbers, and Euler numbers, J. Appl. Math. Vol. 2013 (2013), Article ID 158130, 10 p, jou>

KhanKwong1995, Some invariant and minimum properties of Stirling numbers of the second kind, Fibonacci Quart. 1995 (33,3): 203-205, fibqy>  

Kwasniewski2005, On psi-umbral extensions of Stirling numbers and Dobinski-like formulas, arXiv (20 Oct 2005), aXv>

Lang2000, On generalizations of the Stirling number triangles, J. Integer Seq. Vol. 3 (2000), Article 00.2.4, jis>

Lengyel1994, On the divisibility by 2 of the Stirling numbers of the second kind, Fibonacci Quart. 1994 (32,3): 194-201, fibqy>  

LuoSrivastava2011, Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind, Appl. Math. Comput. Vol. 217, Issue 12, Feb 2011, 5702–5728, gen>

MaltaisGulliver1998, Pascal matrices and Stirling numbers, AppL Math. Lett. Vol. 11, Issue 2, Mar 1998, 7–11, gen>

MansourSchorkShattuck2012, The generalized Stirling and Bell numbers revisited, J. Integer Seq., Vol. 15 (2012), Article 12.8.3, jis>

Pan2012, Matrix decomposition of the unified generalized Stirling nbs. and inversion of the generalized factorial matrices, J. Integer Seq. Vol. 15 (2012), Article 12.6.6, jis>

Pan2013, Convolution properties of the generalized Stirling numbers and the Jacobi-Stirling numbers of the first kind, J. Integer Seq. Vol. 16 (2013), Article 13.9.2, jis>

 

QiGuo2014, Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers, Analysis 2014, 34 (3): 311–317, gen>

ShiraiSato2001, Some identities Involving Bernoulli and Stirling numbers, J. Number Theory Vol. 90, Issue 1, Sep. 2001, 130–142, jou>

Simsek2013a, Generating function for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications, Fixed Point Theory Appl. 2013, 2013: 87, gen>

Simsek2013b, Identities associated with generalized Stirling type numbers and Eulerian type polyn., Math. Comput. Appl. Vol. 18, No. 3, 251-263, 2013, gen>

Sitgreaves1970, Some properties of Stirling numbers of the second kind, The Fibonacci Quarterly 1970 (8,2): 172-181, fibqy>

SixdeniersPensonSolomon2001, Extended Bell and Stirling numbers from hypergeometric exponentiation, J. Integer Seq. Vol. 4 (2001), Article 01.1.4, jis>

Sun Z-W.2007, Combinatorial congruences and Stirling numbers, Acta Arith. 126 (2007), no. 4, 387–398, gen>

Toscano1978, Some results for generalized Bernoulli, Euler, Stirling numbers, Fibonacci Quart. 1978 (16,2): 103-111, fibqy>

Wagner1996, Generalized Stirling and Lah numbers, Discrete Math. Vol. 160, Issues 1–3, 15 Nov 1996, 199–218, gen>

Yang S-L.You2007, On a connection between the Pascal, Stirling and Vandermonde matrices, Discrete Applied Math. Vol. 155, Issue 15, Sep 2007, 2025–2030, gen>

Zeng J.1995, The q-Stirling numbers, continued fractions and the q-Charlier and q-Laguerre polynomials, J. Comp. Appl. Math. Vol. 57, Issue 3, Feb 1995, 413–424, jou>

ZengZhang1994, A q-analog of Newton’s series, Stirling functions and Eulerian functions, Results Math. May 1994, Vol. 25, Issue 3-4, 370-391, gen>

Zhao F-Z.2008, Some properties of associated Stirling numbers, J. Integer Seq. Vol. 11 (2008), Article 08.1.7, jis>

Zhao J.HongZhao W.2014, Divisibility by 2 of Stirling numbers of the second kind and their differences, J. Number Theory, Vol. 140, Jul 2014, 324–348, jou>

Stirling generalized numbers group

Bickel2003, The group of generalized Stirling numbers, Adv. in Appl. Math. Vol. 26, Issue 1, Jan. 2001, 1–22, gen>

stochastic processes

Anshelevich2004a, q- Lévy processes, arXiv (21 Jan 2004), aXv>

BrycWesolowski2004, Conditional moments of q-Meixner processes, arXiv (13 Dec 2004), aXv>

Herzog2013, Brownian motion and Poisson process, Stochastische Systeme, 2013, gen>

 

Lawi2008, Hermite and Laguerre polynomials and matrix valued stochastic processes, Electron. Commun. Probab. 13 (2008), 67–84, gen>

Pommeret2000, Orthogonality of the Sheffer system associated to a Levy process, J. of Statist. Plann. Inference Vol. 86, Issue 1, 15 Apr 2000, 1–10, jou>

Schoutens2001, An application in stochastics of the Laguerre-type polynomials, J. Comp. Appl. Math. Vol. 133, Issues 1–2, 1 Aug 2001, 593–600, jou>

Stam1988, Polynomials of binomial type and compound Poisson processes, J. Math. Anal. Appl. Vol. 130, Issue 2, Mar 1988, 493–508, jou>

succession rules

BacchelliFerrariPinzaniSprugnoli2010, Mixed succession rules: The commutative case, J. Combin. Theory Ser. A, Vol. 117, Issue 5, Jul 2010, 568–582, jou>

DuchiFrosiniPinzaniRinaldi2003, A note on rational succession rules, J. Integer Seq. Vol. 6 (2003), Article 03.1.7, jis>

FerrariPinzani2005, Catalan-like numbers and succession rules, PU.M.A. Vol. 16 (2005), No. 3, 229-250, gen>

Sulanke

Velasco2010, Convolution and Sulanke Numbers, J. Integer Seq. Vol. 13 (2010), Article 10.1.8, jis>

tangent numbers, tanh numbers

Arreghi2001a, Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles, arXiv (17 Sept 2001), aXv>

Della Riccia2004, Inversions relating Stirling, Tanh, Lah numbers and an application to Mathematical Statistics, arXiv (31May 2004), aXv>

Della Riccia2006, Converting between generalized Bell, Lah, Stirling, and Tanh numbers, J. Integer Seq. Vol. 9 (2006), Article 06.3.5, jis>

Donaghey1976, Binomial self-inverse sequences and tangent coefficients, J. Combin. Theory Ser. A, Vol. 21, Issue 2, Sep 1976, 155–163, jou>

Tetranacci

Waddill1992a, The Tetranacci sequence and generalizations, Fibonacci Quart. 1992 (30,1): 9-19, fibqy>

Waddill1992b, Some properties of the tetranacci sequence modulo m, Fibonacci Quart. 1992 (30,3): 232-238, fibqy>

Toda chain

Barry2010b, The restricted Toda chain, exponential Riordan arrays, and Hankel transforms, J. Integer Seq. Vol. 13 (2010), Article 10.8.4, jis>

Barry2014a, Generalized Stirling numbers, exponential Riordan arrays, and Toda chain equations, J. Integer Seq. Vol. 17 (2014), Article 14.2.3, jis>

NakamuraZhedanov2004, Toda Chain, Sheffer class of orthogonal polynomials and combinatorial numbers, Proc. of Institute of Math. of NAS of Ukraine 2004, Vol. 50, Part 1, 450–457, nat>

Toeplitz

Adukov1998, Generalized inversion of block Toeplitz matrices, Linear Algebra App 274: 85-124 (1998), gen>

Adukov1999, Generalized inversion of finite rank Hankel and Toeplitz operators with rational matrix symbols, Linear Algebra App 290 (1999), 119-134, gen>

Basor1978, Asymptotic formulas for Toepliz determinants, Trans. Amer. Math. Soc. Vol. 239, May 1978, nat>

BasorWidom1983, Toeplitz and Wiener-Hopf determinants with piecewise continuous symbols, J. Funct. Anal. Vol. 50, Issue 3, Feb 1983, 387–413, jou>

BasorWidom2000, On a Toeplitz determinant identity of Borodin and Okounkov, arXiv (9 Apr 2000), aXv>

BogoyaBottcherGrudsky2012, Eigenvalues of Hermitian Toeplitz matrices with polynomially increasing entries, J. Spectr. Theory 2 (2012), 267–292, jou>

BottcherGrudsky1999, Toeplitz band matrices with exponentially growing condition numbers, The Electronic J. of Linear Algebra Vol. 5, 104-125, Dec 1999, gen>

BottcherKarlovichSilberman2007, Generalized Krein algebras and asyptotics of Toeplitz determinants, Methods Funct. Anal. Topology Vol. 13 (2007), no. 3, 236–261, gen>

DeiftItsKrasovsky2011, Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities, Annals Math. 174 (2011), 1243-1299, gen>

DeiftItsKrasowski2012, On the asymptotics of a Toeplitz determinant with singulariries, arXix (6 Jun 2012), aXv>

FarenickKrupnickKrupnickLee, Normal Toeplitz matrices, SIAM J. Matrix Anal. Appl. 17(4) · Oct 1996, gen>

FelsnerHeldt2015, Lattice path enumeration and Toeplitz matrices, J. Integer Seq. Vol. 18 (2015), Article 15.1.3, jis>

Finck2014, Hankel and Toeplitz Determinants, Unpublished note, xxxx>

FioreZellini1998, Matrix displacement decompositions and applications to Toeplitz linear systems, Linear Algebra Appl. 268: 197-225 (1998), gen>

HeinigBojanczyk1997, Transformation techniques forToeplitz and Toeplitz-plus-Hankel matrices Part I.Tranformations, Linear Algebra Appl. 254: 193-226 (1997), gen>

HeinigBojanczyk1998, Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices II. Algorithms, Linear Algebra Appl. Vol.278, Issues 1–3, 15 Jul 1998, 11–36, gen>

HeinigRost2002, Split Algorithms and ZW-Factorization for Toeplitz and Toeplitz-plus-Hankel Matrices, Proc. MTNS, Notre Dame 2002, gen>

HeinigRost2004, Split algorithms for skewsymmetric Toeplitz matrices with arbitrary rank profile, Theoretical Comp. Sc. Vol. 315, Issues 2–3, 6, May 2004, 453-468, gen>

HeinigRost2011, Fast algorithms for Toeplitz and Hankel matrices, Linear Algebra Appl. 435 (2011), 1–59, gen>

Krasovsky2011, Aspects of Toeplitz determinants, Progr. Probab. Vol. 64, 2011, 305-324  arXiv (18 Oct 2011), aXv>

LabahnShalom1994, Inversion of Toeplitz structured matrices using only standard equations, Linear Algebra Appl. Vol. 207, Aug 1994, 49–70, gen>

Li2011, On calculating the determinants of Toeplitz matrices, J. Appl. M. Bioinformatics, vol.1, no.1, 2011, 55-64, jou>

LvHuang2007, A note on inversion of Toeplitz matrices, Applied Math. Letters Vol. 20, Issue 12, Dec 2007, 1189–1193, gen>

LvHuang2013, The inverses of block Toeplitz matrices, J. of Math. Vol. 2013 (2013), Article ID 207176, 8 p, jou>

MukherjeeMaiti1988, On Some Properties of Positive Definite Toeplitz Matrices and Their Possible Applications , Linear Algebra Appl. 102: 211-240 (1988), gen>

Musicus1988, Levinson and fast Choleski algorithms for Toeplitz and almost Toeplitz matrices, RLE Technical Report No. 538, gen>

Trench2009, Banded symmetric Toeplitz matrices: where linear algebra borrows from difference equations, Trinity University Math. Seminar 2009, gen>

Widom1974, Asymptotic behavior of block Toeplitz matrices and determinants, Adv. Math. Vol. 13, Issue 3, Jul 1974, 284–322, gen>

Widom1976, Asymptotic behavior of block Toeplitz matrices and determinants. II, Adv. Math. Vol. 21, Issue 1, Jul 1976, 1–29, gen>

YeLim2015, Every matrix is a product of Toeplitz matrices, Found. Comp. Math. (Mar 2015), gen>

ZhuWakin2016, On the asymptotic equivalence of circulant and Toeplitz matrices, arXiv (Aug 2016), aXv>

Toeplitz-plus-Hankel

AdukovIbryaeva2005, Generalized inversion of Toeplitz-plus-Hankel matrices, arXiv (2 Mar 2005), aXv>

AdukovIbryaeva2012, Inversion of the Toeplitz-plus-Hankel matrices via generalized inversion, Int. J. Pure Appl. Math. 79 No. 1 2012, 57-65, gen>

BarryHennessy2012b, Riordan arrays and the LDU decomposition of symmetric Toeplitz plus Hankel matrices, Linear Algebra Appl. Vol. 437, Issue 6, Sep 2012, 1380–1393, gen>

BasorEhrhardt2009, Determinant computations for some classes of Toeplitz-Hankel matrices, Oper. Matrices, 2009 (vol.3,2): 167-186, gen>

BevilacquaBonanniBozzo1995, On algebras of Toeplitz plus Hankel matrices, Linear Algebra Appl. 223/224: 99-118 (1995), gen>

Fasino1996, Spectral properties of Toeplitz-plus-Hankel matrices, Calcolo 33(1):87-98 · Jun 1996, gen>

Heinig2002, Kernel structure of Toeplitz-plus-Hankel matrices, Linear Algebra  Appl. Vol. 340, Issues 1–3, 1 Jan 2002, 1–13, gen>

HeinigBojanczyk1997, Transformation techniques forToeplitz and Toeplitz-plus-Hankel matrices Part I.Tranformations, Linear Algebra Appl. 254: 193-226 (1997), gen>

HeinigBojanczyk1998, Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices II. Algorithms, Linear Algebra Appl. Vol.278, Issues 1–3, 15 Jul 1998, 11–36, gen>

HeinigRost1988, On the inverses of Toeplitz-plus-Hankel matrices, Linear Algebra Appl. Vol. 106, Aug 1988, 39-52, gen>

HeinigRost1989, Matrlx representations of Toeplitz-plus-Hankel matrix inverses, Linear Algebra Appl.Vol. 113, Feb 1989, 65­-78, gen>

HeinigRost1998, Representations of Toeplitz-plus-Hankel matrices using trigonometric transformations with application to fast matrix-vector multiplication, Linear Algebra Appl. Vol. 275–276, May 1998, 225-248, gen>

HeinigRost2002, Split Algorithms and ZW-Factorization for Toeplitz and Toeplitz-plus-Hankel Matrices, Proc. MTNS, Notre Dame 2002, gen>

KuKuo1993, Preconditioned iterative methods for solvind Toeplitz-plus-Hankel systems, SIAM J. Num. Anal. Vol. 30. No. 3, 824-825, Jun 1993, gen>

März2014, Functions of difference matrices are Toeplitz plus Hankel, SIAM Review 56.No.3 (2014), p 525-546, gen>

StrangMacNamara2016, Functions of difference matrices are Toeplitz plus Hankel, Siam Review, Vol. 56, No. 3, 2016, 525–546, gen>

Touchard

Chrysaphinou1985, On Touchard polynomials, Discrete Math. Vol. 54, Issue 2, Apr 1985, 143-152, gen>

Gould1977, Generalization of a formula of Touchard for Catalan numbers, J. Combin. Theory Ser. A, Vol. 23, Issue 3, Nov 1977, 351–353, jou>

 

MansourSchork2013, The generalized Touchard polynomials revisited, Appl. Math. Comput. Vol. 219, Issue 19, Jun 2013, 9978–9991, gen>

MihoubiMaamra2011, Touchard polynomials, partial Bell polynomials and polynomials of binomial type, J. Integer Seq. Vol. 14 (2011), Article 11.3.1, jis>

Transforms

ArmasSethuraman2008, A Note on the Hankel Transform of the Central Binomial Coefficients, J. Integer Seq. Vol. 11 (2008), Article 08.5.8, jis>

AskeyRahmanSuslov1996, On a general q-Fourier transformation with

nonsymmetric kernels, J. Comp. Appl. Math. Vol. 68, Issues 1–2,Apr1996, 25-

55, jou>

AustinBantilanEggeJonasKory2009, The Pfaffian transform, J. Integer Seq. Vol. 12 (2009), Article 09.1.5, jis>

Barry2007b, Some observations on the Lah and Laguerre transforms of integer sequences, J. Integer Seq. Vol. 10 (2007), Article 07.4.6, jis>

Barry2010a, Generalized Catalan numbers, Hankel transforms and Somos-4 sequences, J. Integer Seq. Vol. 13 (2010), Article 10.7.2, jis>

Barry2010b, The restricted Toda chain, exponential Riordan arrays, and Hankel transforms, J. Integer Seq. Vol. 13 (2010), Article 10.8.4, jis>

Barry2011a, Riordan arrays, orthogonal polynomials as moments, and Hankel transforms, J. Integer Seq. Vol. 14 (2011), Article 11.2.2, jis>

Barry2011c, Combinatorial polynomials as moments, Hankel transforms, and exponential Riordan arrays, J. Integer Seq. Vol. 14 (2011), Article 11.6.7, jis>

BarryHennessy2009, Notes on a family of Riordan arrays and associated integer Hankel transforms, J. Integer Seq. Vol. 12 (2009), Article 09.5.3, jis>

Bouras2013, A new characterization of Catalan numbers related to Hankel transforms and Fibonacci numbers, J. Integer Seq. Vol. 16 (2013), Article 13.3.3, jis>

ChamberlandFrench2007, Generalized Catalan numbers and generalized Hankel transformations, J. Integer Seq. Vol. 10 (2007), Article 07.1.1, jis>

 Coffey2006, Special functions and the Mellin transforms of Laguerre and Hermite functions, arXiv ( 28 Dec 2006),  aXv>

Corcino R.B.Jaylo-CamposMacodi-Ringia2014, On noncentral Bell numbers and their Hankel transforms, Turkish J. of Analysis and Number Theory 2014, Vol. 2, No. 2, 28-35, nat>

CvetkovicRajkovicIvkovic2002, Catalan numbers, the Hankel transform, and Fibonacci numbers, J. Integer Seq. Vol. 5 (2002), Article 02.1.3, jis>

Dhaouadi2013, On the q-Bessel Fourier transform, Bull. Math. Anal. Appl. Vol. 5 Issue 2 (2013), 42-60, nat>

DoughertyFrenchSaderholmQian2011, Hankel transforms of linear combinations of Catalan numbers, J. Integer Seq. Vol. 14 (2011), Article 11.5.1, jis>

French2007, Transformations preserving the Hankel transform, J.Integer Seq. Vol. 10 (2007), Article 07.7.3, jis>

Glaeske2000, Convolution structure of (generalized) Hermite transforms, Banach Center Publ. Vol. 53, nat>

Groenevelt2003a, The Wilson function transform, arXiv (30 Jun 2003), aXv>

Groenevelt2009, The vector-valued big q-Jacobi transform, Constr. Approx. (2009) 29:  85–127,  gen>

Haukkanen1997b, A note on the bracket function transform, Fibonacci Quart. 1997 (35,2): 156-159, fibqy>

HeinigBojanczyk1997, Transformation techniques forToeplitz and Toeplitz-plus-Hankel matrices Part I.Tranformations, Linear Algebra Appl. 254: 193-226 (1997), gen>  

HeinigBojanczyk1998, Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices II. Algorithms, Linear Algebra Appl. Vol.278, Issues 1–3, 15 Jul 1998, 11–36, gen>

IsmailRahmanSuslov1997, Some summation theorems and transformations for q-series, Can. J. Math. Vol. 49 (3), 1997, 543–567, nat>

Ivic2008, The Laplace and Mellin transforms of powers of the Riemann zeta-function, arXiv (2 Jun 2006), aXv>

IvicJutilaMotohashi2000, The Mellin transform of powers of the zeta-function, Acta Arithmetica, XCV.4 (2000), gen>

JinDickinson2000, Apéry sequences and Legendre transforms, J. Austral. Math. Soc. (Series A) 68 (2000), 349-356, nat>

Kimberling2003, Matrix transformations of Integer Sequences, J. Integer Seq. Vol. 6 (2003), Article 03.3.3, jis>

Koornwinder1975, A new proof of a Paley-Wiener type theorem for the Jacobi transform, Arkiv för Matematik, 1975, Vol. 13, Issue 1-2, 145-159, nat>

KoornwinderSwarttouw1992, On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. Vol. 333, No. 1, Sep 1992, nat>

Layman2001, The Hankel transform and some of its properties, J. Integer Seq. Vol. 4 (2001), Article 01.1.5, jis>

LuchkoKiryakova2013, The Mellin integral transform in fractional calculus, Fract. Calc. Appl. Anal. Vol. 16, No. 2, (2013), gen>

MillerSrivastava1998, On the Mellin transform of a product of hypergeometric functions, J. Austral. Math. Soc. Ser. B 40(1998), 222–237, nat>

Nikolova2012, α-Mellin transform and one of its applications, Mathematica Balkanica, New Series Vol. 26, 2012, Fasc. 1-2, nat>

Oosthuisen2011, The Mellin transform, This project is supported by the National Research Foundation (NRF) (2011), gen>

PetkovicRajkovic2006, Hankel transform of Narayana polynomials and generalized Catalan numbers, Int. Conference PRIM 2006, gen>

PetkovicRajkovicBarry2011, The Hankel transform of generalized central trinomial coefficients and related sequences, Integral Transforms Spec. Funct. 2011 (vol.22,1): 29-44, gen>

Piessens2000, The Hankel transform, Ch. 9, A. D. Poularikas, Editor-in-Chief, Transforms and Applications Handbook (Third Edition 2000), gen>

PilipovicStojanovic1992, The modified Mellin transform and convolution, Univ. U Novom Sadu Zb. Ser. Mat. 22,2 (1992), 109-126, nat>

PurohitKalla2007, On q-Laplace transforms of the q-Bessel functions, Fract. Calc. Appl. Anal. Vol. 10, No. 2, (2007), 189-196, gen>

RajkovicPetkovićBarry2007, The Hankel transform of the sum of consecutive generalized Catalan numbers, Integral Transforms and Special Functions, Vol. 18, Issue 4, 2007, aXv>

Schmidt1995, Legendre transforms and Apéry's sequences, J. Austral. Math. Soc. (Series A) 58 (1995), 358-375, nat>

SharmaDeshmukh2014, Applications of two dimensional fractional Mellin transform, Int. J. Scient. Innov. Math. Research, Vol. 2, Issue 9, Sep 2014, 794-799, gen>

SpiveySteil2006, The k-binomial transforms and the Hankel transform, J. Integer Seq. Vol. 9 (2006), Article 06.1.1, jis>

Strang2010, Fast transforms: banded matrices with banded inverses, Proc. Natl. Acad. Sci. USA, 107 (#28), (2010) 12413-12416, nat>

Strehl1992, Recurrences and Legendre Transform, Sém. Lothar. Combin. B29b (1992), 22 p. 29 Thurnau, Sep 1992, gen>

TwamleyMilburn2007, The quantum Mellin transform, arXiv (12 Feb 2007), aXv>

Tribonacci

AtanassovHleBarskaMihov1992, Recurrent formulas of the generalized Fibonacci and Tribonacci sequences, Fibonacci Quart. 1992 (30,1): 77-79, fibqy>

Cereceda2014, Determinantal representations for generalized Fibonacci and tribonacci numbers, Int. J. Contemp. Math. Sci. Vol. 9, 2014, no. 6, 269 - 285, gen>

Edwards2008-09, A Pascal-like triangle related to the tribonacci numbers, Fibonacci Quart. 2008-09 (46-47,1): 18-25,  fibqy>

Elia2001, Derived sequences, the tribonacci recurrence and cubic forms, Fibonacci Quart. 2001 (39,2): 107-115, fibqy>

Feinberg1963, Fibonacci-Tribonacci, Fibonacci Quart. 1963 (1,3): 71-74, fibqy>

Howard2001, A tribonacci identity, Fibonacci Quart. 2001 (39,4): 352-357, fibqy>

KiliçProdinger2014, A note on the conjecture of Ramirez and Sirvent, J. of Integer Seq. Vol. 17 (2014), Article 14.5.8, jis>

MansourShattuck2013b, Polynomials whose coefficients are generalized Tribonacci numbers, Appl. Math. Comput. Vol. 219, Issue 15, Apr 2013, 8366–8374, gen>

McCarty1981, A formula for tribonacci numbers, Fibonacci Quart. 1981 (19,5): 391-393, fibqy>

Tribonacci-Lucas

YilmazTaskara2014, Incomplete Tribonacci-Lucas numbers and polynomials, arXiv (16 Apr 2014), aXv>

ultraspherical (see also Gegenbauer)

Anshelevich2011, A characterization of ultraspherical polynomials, arXiv (3 Aug 2011), aXv>

AskeyKoornwinderRahman1986, An integral of products of ultraspherical functions and q-extensions, J. Lond. Math. Soc. (2) (1986) 33 (1): 133-148, nat>

Chatterjea1969, Bilateral generating function for the ultraspherical polynomials, Pacific J. Math. Vol. 29, No. 1 (1969), 73-76, nat>

Demni2009, Ultrasherical type generating functions for orthogonal polynomials, Probab. Math. Statist. Vol. 29, Fasc. 2 (2009), 281-296, gen>

GrozaKachuryk2006, On orthogonality relations for dual discrete q-ultraspherical polynomials, SIGMA Symmetry Integrability Geom. Methods Appl. Vol. 2 (2006), Paper 034, 8 p,  gen>

Koelink1995, Identities for q-ultraspherical polynomials and Jacobi functions, Proc. Amer. Math. Soc. 123 (1995), 2479-2487, nat>

Koornwinder1990, Jacobi functions as limit cases of q-ultraspherical polynomials, J. Math. Anal. and Appl. Vol. 148, Issue 1 (May 1990) 44-54, jou>

PacharoniZurrian2014, Matrix ultraspherical polynomials: the 2 × 2  fundamental cases, arXiv (31 may 2014), aXv>

Umbral calculus
Agapito2010, A classical umbral view of the Riordan group and related Sheffer sequences, Algebra and Combinatorics Seminar, Nov 26, 2010, gen>

AgapitoMestrePetrulloTorres2011, Riordan arrays and applications via the classical Umbral Calculus, arXiv (30 Mar 2011), aXv>

AgapitoMestrePetrulloTorres2013, A symbolic treatment of Riordan arrays, Linear Algebra App. Vol. 439, Issue 7, Oct 2013, 1700–1715, gen>

AraciKongAcikgozSen2014, A new approach to multivariate q-Euler polynomials using the umbral calculus, J. Integer Seq. Vol. 17 (2014), Article 14.1.2, jis>

BarnabeiBriniNicoletti1982, Recursive matrices and umbral calculus, J. Algebra Vol. 75, Issue 2, Apr 1982, 546–573, jou>

Bell1934, Exponential numbers, Amer. Math. Monthly, Vol. 41, No. 7, (Aug. - Sep., 1934),  411-419, nat>

Bell1940, Postulational bases for the umbral calculus, Amer. J. Math. Vol. 62, No. 1/4 (1940), 717-724, nat>

Cigler1978, Some remarks on Rota's umbral calculus, Mathematics- Indagationes Mathematicae (Proceedings) Vol. 81, Issue 1, 1978, 27–42, gen>

DattoliRicciCesarano2003, The Lagrange polynomials, the associated generalizations, and the umbral calculus, Integral Transforms Spec. Funct. Vol. 14, Issue 2, 2003, gen>

DereSimsek2011a, Unification of the three families of generalized Apostol type polynomials on the umbral algebra, arXiv (7 Oct 2011), aXv>

DereSimsek2011b, Genocchi polynomials associated with the umbral algebra, Appl. Math. Comput. Vol. 218, Issue 3, Oct 2011, 756–761, gen>

Di Bucchianico1998, An introduction to umbral Calculus, Euler Institute for Discrete Mathematics and its Applications,  gen>

Di BucchianicoLoebWagner2000, A selected survey of umbral Calculus, Electron. J. Combin. #DS3 Update of April, 2000, gen>

Di NardoNiederhausenSenato2009, The classical umbral calculus: Sheffer sequences, Lect. Notes Semin. Interdiscip. Mat. Vol. 8 (2009), 101–130, gen>

Di NardoSenato2006, An umbral setting for cumulants and factorial moments, European J. Combin. Vol. 27, Issue 3, Apr 2006, 394–413, gen>

Ernst2006, q-Bernoulli and q-Euler polynomials, an umbral approach, Int. J. Differ. Equ. Vol. 1, No. 1, (2006), 31–80, gen>

Ernst2008a, q-Stirling numbers, an umbral approach, Adv. Dyn. Syst. Appl. Vol. 3, No. 2, 251–282 (2008), gen>

Ernst2008b, q-Pascal and q-Bernoulli matrices, an umbral approach, U.U.D.M. Report 2008:23, gen>

Ernst2013, An umbral approach to find q-analogues of matrix formulas,  Linear Algebra Appl. Vol. 439, Issue 4, Aug 2013, 1167–1182, gen>

Gessel2003, Applications of the classical umbral calculus, Algebra Universalis 2003 (vol.49,4): 397-434, gen>

Guinand1979, The umbral method: a survey of elementary mnemonic and manipulative uses, Amer. Math. Monthly,  Vol. 86, No. 3 (Mar 1979), 187-195, nat>

HeHsuShiue2008, A symbolic operator approach to several summation formulas for power series II, Discrete Math. Vol. 308, Issue 16, 28 Aug 2008, 3427–3440, gen>

HeHsuShiueTorney2005, A symbolic operator approach to several summation formulas for power series, J. Comp. Appl. Math. Vol. 177, Issue 1, 1 May 2005, 17–33, jou>

IhrigIsmail1981, A q-umbral calculus, J. Math. Anal. Appl. Vol. 84, Issue 1, Nov 1981, 178–207, jou>

KeleshteriMahmudov2015, A q-umbral approach to q-Appell polynomials, arXiv (19 May 2015), aXv>

Kim D.S.Kim T.2014b, Some properties of higher-order Daehee polynomials of the second order arising from umbral calculus, J. Inequal. Appl. 2014, 2014:195, jou>

Kim D.S.Kim T.2015, Umbral calculus associated with Bernoulli polynomials, J. Number Theory 147 (2015), 871–882, jou>

KimKim2012a, Applications of umbral calculus associated with p-adic invariant integrals on Zp, Abstr. Appl. Anal. Vol. 2012 (2012), Article ID 865721, 12 pages,  gen>

KimKim2012e, Some identities of Frobenius-Euler polynomials arising from umbral calculus, Adv. Difference Equ. 2012, 2012: 196, gen>

KimKim2013d, Some identities arising from Sheffer sequences for the powers of Sheffer pairs under umbral calculus, arXiv (29 Mar 2013), aXv>

KimKimDolgyRim2013, Some identities of higher-order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus, J. Inequal. Appl. 2013, 2013:211, jou>

KimKimLee2013a, A note on poly-Bernoulli polynomials arising from umbral calculus, Adv. Studies Theor. Phys. Vol. 7, 2013, no. 15, 731-744, gen>

KimKimLee2013b, Some identities arising from Sheffer sequences for the powers of Sheffer pairs under umbral composition, Appl. Math. Sci. (Ruse) Vol. 7, 2013, no. 106, 5287-5299, gen>

KimKimLeeDolgyRim2011, Some new identities on the Bernoulli and Euler numbers, Discrete Dyn. Nat. Soc. Vol. 2011, Article ID 856132, 11 p, gen>

KimKimLeeRim2013, Some identities of Bernoulli, Euler and Abel polynomials arising from umbral calculus, Adv. Difference Equ. 2013, 2013: 15, gen>

KimKimMansourRimSchork2013, Umbral calculus and Sheffer sequences of polynomials, J. Math. Phys. 54, 083504 (2013), jou>

KimKimRim2014, Some identities of polynomials arising from umbral calculus, J. Comput. Anal. Appl. Jan 2014, Vol. 16, Issue 1, 293-306, aXv>

KimKimRimDolgy2013b, Some identities of Frobenius-type Eulerian polynomials arising from umbral calculus, Int. J. Math. Anal. (Ruse), Vol. 7, 2013, no. 53, 2637-2644, gen>

KimMansour2014, Umbral calculus associated with Frobenius-type Eulerian polynomials, Russ. J. Math. Phys. Jun 2014, Vol. 21, Issue 4, 484-493, nat>

Kwasniewski2004b, First contact remarks on umbral difference calculus references streams, arXiv (8 Mar 2004), aXv>

Kwasniewski2005, On  psi-umbral extensions of Stirling numbers and Dobinski-like formulas, arXiv (20 Oct 2005), aXv>

LuXiangLuo2013, Some results for Apostol-type polynomials associated with umbral algebra, Adv. Difference Equ. 2013, 2013: 201, gen>

Petrullo2009, Cumulants and classical umbral calculus, 62nd Sém. Lothar. Combin.  Heilsbronn (Germany), Feb 22-25, 2009, gen>

PradaSeniosain2004, The classical umbral calculus: reading Blissard with the key given by G. C. Rota and B. D. Taylor, Far East J. Math. Sci. (FJMS) Vol. 12, Issue 1, 121-136 (Jan 2004), nat>

Ray1998, Universal constructions in umbral calculus, Progress in Math. Vol. 161, 1998, 343-357, gen>

Razpet1990, An application of the umbral calculus, J. Math. Anal. and Appl. Vol. 149, Issue 1, Jun 1990, 1–16, jou>

Roman1982a, The theory of the umbral Calculus. I, J. Math. Anal. Appl. Vol. 87, No. 1, 1982, jou>

Roman1982b, The theory of the umbral Calculus. II, J. Math. Anal. Appl. Vol. 89, Issue 1, Sep 1982, 290–314, jou>

Roman1983, The theory of the umbral Calculus. III, J. Math. Anal. Appl. Vol. 95, Issue 2, Sep 1983, 528-563, jou>

Roman1985, More on the umbral calculus, with emphasis on the q-umbral calculus, J. Math. Anal. Appl. Vol. 107, Issue 1, Apr 1985, 222–254, jou>

RomanRota1978, The umbral Calculus, Adv. Math. Vol. 27, No.2 , Feb 1978, 95-188, gen>

RotaTaylor1994, The classical umbral calculus, SIAM J. Math. Anal.  Vol. 25 Issue 2, 1994, 694-711, gen>

SrivastavaNisarKhan2014, Some umbral calculus presentations of the Chan-Chyan-Srivastava polynomials. and the Erkus-Srivastava polynomials, Proyecciones, Vol. 33, No 1, 77-90, Mar 2014, gen>

Taylor2001, Umbral presentations for polynomial sequences, Comput. Math. Appl. Vol. 41, Issue 9, May 2001, 1085–1098, gen>

van der Laan

KaygisizSahin2013a, Generalized Van der Laan and Perrin polynomials, and generalizations of Van der Laan and Perrin numbers, Selçuk J. Appl. Math. Vol. 14. No. 1. 89-103, 2013, nat>

Vandermonde

BenjaminDresden2007, A combinatorial proof of Vandermonde's determinant, Amer. Math. Monthly, Vol. 114, No. 4, 338-341, Apr 2007, nat>

FasinoInglese!992, On the spectral condition of rectangular Vandermonde matrices, Calcolo Sep 1992, Vol. 29, Issue 3, 291–300, gen>

Gautshi1983, The condition of Vandermonde-like matrices involving orthogonal polynomials, Linear Algebra Appl. 52/53, 293-300 (1983), gen>

Oruç2007, LU factorization of the Vandermonde matrix and its applications, Applied Math. Letters Vol. 20, Issue 9, Sep 2007, 982–987, gen

Yang S-l.2005, On the LU factorization of the Vandermonde matrix, Discrete Applied Math. 146 (2005) 102–105, gen>

Yang S-L.You2007, On a connection between the Pascal, Stirling and Vandermonde matrices, Discrete Applied Math. Vol. 155, Issue 15, Sep 2007, 2025–2030, gen>

Vieta, Vieta-Jacobsthal, Vieta-Pell polynomials

Horadam2002b, Vieta polynomials, Fibonacci Quart.y 2002 (40,3): 223-232, fibqy>

YalçinTasciErkus-Duman2015, Generalized Vieta-Jacobsthal and Vieta-Jacobsthal-Lucas polynomials, Math. Commun. 20(2015), 241–251, gen>

YalçinTasciErkus-Duman2015, Generalized Vieta-Jacobsthal and Vieta-Jacobsthal-Lucas polynomials, Math. Commun. 20(2015), 241–251, gen>

Vieta-Jacobsthal-Lucas, Vieta-Pell_Lucas polynomials

TasciYalcin2013, Vieta-Pell and Vieta-Pell-Lucas polynomials, Adv. Difference Equ. 2013, 2013: 224, gen>

YalçinTasciErkus-Duman2015, Generalized Vieta-Jacobsthal and Vieta-Jacobsthal-Lucas polynomials, Math. Commun. 20(2015), 241–251, gen>

Weierstrass

Brizard2015, Notes on the Weierstrass elliptic function, aXv (27 Oct 2015), aXv>

BrownawellKubota1977, The algebraic independence of Weierstrass functions and some related numbers, Acta Arith. LXXXII.2 (1997), gen>

Chandrasekharan1985, The zeta­function and the sigma­function of Weierstrass, Grundlehren der mathematischen Wissenschaften Vol. 281 Elliptic Functions (1985), p 48-­57, gen>

DukeImamoglu2008, The zeros of the Weierstrass –function and hypergeometric series, Mathematische Annalen 340(4): 897-905 · Apr 2008, nat>

EichlerZagier1982, On the Zeros of the Weierstrass p-Function, Math. Ann. 258, 399-407 (1982), gen>

EilbeckEnglandOnishi2014, Some new addition formulae for Weierstrass elliptic functions, arXiv (2 Aug 2014), aXv>

England2007, The Weierstrass theory for elliptic functions, including the generalisation to higher genus, The Burn 2007, gen>

Wiener chaos

AlbeverioHerzberg2008, The moment problem on the Wiener space, Bull. Sci. math. 132 (2008) 7–18, nat>

Anshelevich2004a, q- Lévy processes, arXiv (21 Jan 2004), aXv>

CayamaGonzalez-Parra2013, Application of polynomial chaos to random partial differential equations, Revista Ciencia e Ingeniería Vol. 34, No. 2, 2013, 101-110, nat>

ImRyu2002, An analogue of Wiener measure and its applications, J. Korean Math. Soc. 39 (2002), No. 5, p 801–819, nat>

Wiener1938, The Homogeneous Chaos, Amer. J. Math. Vol. 60, No. 4 (Oct 1938), 897-936, nat>

XiuKarniadaris2002, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput. 24 (2), 619–644, gen>

Wythoff number, pair

Bicknell-Johnson1985, Generalized Wythoff numbers form simultaneous Fibonacci representations, Fibonacci Quart. 1985 (23,4): 308-318, fibqy>

Hoggatt, Jr.Hillman1978, A property of Wythoff pairs, Fibonacci Quart. 1978 (16,5): 472, fibqy>

Horadam1978, Wythoff pairs, Fibonacci Quart. 1978 (16,2): 147-151, fibqy>

Zernike

AharmimHamyaniWassouliGhanmi2013, New operational formulas and generating functions for the generalized Zernike polynomials, arXiv (12 Dec 2013), aXv>

z-function (see also Riemann)

AraciBagdasaryanOzelSrivastava2014, New symmetric identities involving q-zeta type functions, Appl. Math. Inf. Sci. 8, No. 6, 2803-2808 (2014), gen>

ByrnesJiuMollVignat2013, Recursion rules for the hypergeometric zeta function, arXiv (8 May 2013), gen>

CandelpergherCoppo2012, A new class of identities involving Cauchy numbers, harmonic numbers and zeta values, Ramanujan J. April 2012, Volume 27, Issue 3, 305-328, gen>

Chandrasekharan1985, The zetafunction and the sigmafunction of Weierstrass, Grundlehren der mathematischen Wissenschaften Vol. 281 Elliptic Functions (1985), p 48-57, gen>

Chu1997a, Hypergeometric series and the Riemann zeta function, Acta Arith. LXXXII.2 (1997), gen>

HassenNguyen2005, Hypergeometric zeta functions, arXiv (27 Sep 2005), aXv>

IbrahimDarus2011, On operator defined by double zeta functions, Tamkang J. Math. Vol. 42, No. 2, 163-174, Summer 2011, aXv>

Ivic2008, The Laplace and Mellin transforms of powers of the Riemann zeta-function, arXiv (2 Jun 2006), aXv>

Kim2006b, q-analogue of Euler- Barnes multiple zeta functions, arXiv (6 Mar 2006), aXv>

Kim2009a, q-Euler numbers and polynonials associated with multiple q-zeta functions, arXiv (24 Dec 2009), aXv>

Kim2009b, Barnes type multiple q-zeta functions and q-Euler polynomials, arXiv (28 Dec 2009), aXv>

KimRimSimsekKim2008, On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions, J. Korean Math. 45 (2008), No. 2, 435-453, nat>

KimRyooJangRim2005, Exploring the q-Riemann zeta function and q-Bernoulli polynomials, Discrete Dyn. Nat. Soc. Vol. 2005 (2005), Issue 2, 171-181, gen>

KimSimsek2005, Barnes’ type multiple Changhee q-zeta functions, arXiv (10 Fev 2005), aXv>

KimSimsekSrivastava2005, q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, arXiv (1 Fev 2005), aXv>

Laurincikas2010, Universality of the Riemann zeta-function, J. Number Theory Vol. 130, Issue 10, Oct 2010, 2323–2331, aXv>

Soria-LorenteCumbrera-Gonzales2014, q-hypergeometric representations of the q-analogue of zeta function, J. of Fractional Calculus and Applications Vol. 5 (2) Jul 2014, 1-8, jou>

Soundrarajan2009, Moments of the Riemann z-function, Ann. of Math. (2), 170 (2009), 981–993, nat>

Sury2003, Bernoulli numbers and the Riemann zeta function, Resonance Jul 2003, Vol. 8, Issue 7, 54-62, gen>