Bivariate generating functions for Rogers–Szegö polynomials

Cao, Jian

doi:10.1016/j.amc.2010.07.021

Cited by 11 publications

(6 citation statements)

References 19 publications

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“…We also deduce a bilinear generating function for the Al-Salam-Carlitz polynomials ψ (α) n (x|q) as an application of the Srivastava-Agarwal type generating functions. (3.20) in [25] and Equation (5.4) in [26]). Each of the following generating relations holds true:…”

Section: The Srivastava-agarwal Type Bilinear Generating Functions For the Generalizedmentioning

confidence: 99%

A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

Srivástava

2021

Mathematics

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Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in this paper, we introduce a general family of q-hypergeometric polynomials and investigate several q-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of q-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized q-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various q-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional parameter p is obviously redundant.

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Section: The Srivastava-agarwal Type Bilinear Generating Functions For the Generalizedmentioning

confidence: 99%

A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

Srivástava

2021

Mathematics

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“…While Cao [6] used the technique of exponential operator decomposition, Srivastava and Agarwal [23] adopted the method of transformation theory to deduce the following results (For more information, please refer to [12,13,2,23,4,5,6]:…”

Section: Mixed Generating Function For Generalized Q-polynomialsmentioning

confidence: 99%

Generalized q-difference equations for general q-polynomials with double q-binomial coefficients

Cao¹,

Hounkonnou²

2021

Preprint

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In this paper, we use the generalized q-polynomials with double q-binomial coefficients and homogeneous q-operators [J. Difference Equ. Appl. 20 (2014), 837-851.] to construct q-difference equations with seven variables, which generalize recent works of Jia et al [Symmetry 2021[Symmetry , 13, 1222. In addition, we derive Rogers formulas, extended Rogers formulas and Srivastava-Agarwal type bilinear generating functions for generalized qpolynomials, which generalize generating functions for Cigler's polynomials [J. Difference Equ. Appl. 24 (2018), 479-502.]. Finally, we also derive mixed generating functions using q-difference equations.

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“…For more references on the -difference operators, see [1,[5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Theorem 2 Consider the Followingunclassified

Some New Generating Functions forq-Hahn Polynomials

Zhou

Luo

2014

Journal of Applied Mathematics

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Bivariate generating functions for Rogers–Szegö polynomials

Cited by 11 publications

References 19 publications

A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

Generalized q-difference equations for general q-polynomials with double q-binomial coefficients

Some New Generating Functions forq-Hahn Polynomials

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