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

Autor:	Srivastava, Hari Mohan, Cao, Jian, Arjika, Sama
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics Mathematics - Functional Analysis Mathematics - Number Theory 05A30 11B65 33D15 33D45 33D60 39A13 39B32
Zdroj:	Symmetry 2020, 12, 1816 (2020)
Druh dokumentu:	Working Paper
DOI:	10.3390/sym12111816
Popis:	In this paper, we use two $q$-operators $\mathbb{T}(a,b,c,d,e,yD_x)$ and $\mathbb{E}(a,b,c,d,e,y\theta_x)$ to derive two potentially useful generalizations of the $q$-binomial theorem, a set of two extensions of the $q$-Chu-Vandermonde summation formula and two new generalizations of the Andrews-Askey integral by means of the $q$-difference equations. We also briefly describe relevant connections of various special cases and consequences of our main results with a number of known results. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.15118 Zobrazit plný text záznamu View this record from Arxiv