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

2021/12/17 by Cao, Jian, Arjika, Sama, Hounkonnou, Mahouton Norbert
#11B65 #2010 Mathematics Subject Classification: Primary: 05A30 #33D15 #33D45 #Combinatorics (math.CO) #FOS: Mathematics #Secondary: 05A40

paper · doi:10.48550/arxiv.2112.12075

Abstract

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, 13, 1222.]. In addition, we derive Rogers formulas, extended Rogers formulas and Srivastava--Agarwal type bilinear generating functions for generalized q-polynomials, 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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