English

A Note on Generalized $q$-Difference Equations and Their Applications Involving $q$-Hypergeometric Functions

Combinatorics 2020-11-03 v1 Functional Analysis Number Theory

Abstract

In this paper, we use two qq-operators T(a,b,c,d,e,yDx)\mathbb{T}(a,b,c,d,e,yD_x) and E(a,b,c,d,e,yθx)\mathbb{E}(a,b,c,d,e,y\theta_x) to derive two potentially useful generalizations of the qq-binomial theorem, a set of two extensions of the qq-Chu-Vandermonde summation formula and two new generalizations of the Andrews-Askey integral by means of the qq-difference equations. We also briefly describe relevant connections of various special cases and consequences of our main results with a number of known results.

Keywords

Cite

@article{arxiv.2010.15118,
  title  = {A Note on Generalized $q$-Difference Equations and Their Applications Involving $q$-Hypergeometric Functions},
  author = {Hari Mohan Srivastava and Jian Cao and Sama Arjika},
  journal= {arXiv preprint arXiv:2010.15118},
  year   = {2020}
}

Comments

17 pages

R2 v1 2026-06-23T19:43:22.658Z