English

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

Combinatorics 2021-12-23 v1

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.

Keywords

Cite

@article{arxiv.2112.12075,
  title  = {Generalized q-difference equations for general q-polynomials with double q-binomial coefficients},
  author = {Jian Cao and Sama Arjika and Mahouton Norbert Hounkonnou},
  journal= {arXiv preprint arXiv:2112.12075},
  year   = {2021}
}
R2 v1 2026-06-24T08:28:21.273Z