Abstract
Our investigation is motivated essentially by the demonstrated applications of the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, in many diverse areas. Here, in this paper, we use two q-operators T(a,b,c,d,e,yDx) and E(a,b,c,d,e,yθx) 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.
Highlights
If we first set i + j = m and extract the coefficients of u from the (v, w; q)m two members of the assertion (56) of Theorem 4, we obtain the transformation formula (57), which leads us to the q-Chu-Vandermonde summation Formula (55) when m = 0
The following famous formula is known as the Andrews-Askey integral
It is believed that the q-series and q-integral identities, which we have presented in this paper, as well as the various related recent works cited here, will provide encouragement and motivation for further researches on the topics that are dealt with and investigated in this paper
Summary
International Chair of Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, Post Office Box 072, Cotonou 50, Benin. Received: October 2020; Accepted: 30 October 2020 ; Published: 2 November 2020
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
