A General Family of $q$-Hypergeometric Polynomials and Associated Generating Functions

Abstract

In this paper, we introduce a general family of $q$-hypergeometric polynomials and investigate several $q$-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of $q$-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized $q$-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various $q$-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called $(p,q)$-variations of the $q$-results, which we have investigated here, because the additional parameter $p$ is obviously redundant.

14 pages

References in corpus (3)

• A Note on Generalized $q$-Difference Equations and Their Applications Involving $q$-Hypergeometric Functions
• A note on generalized $q$-difference equations for general Al-Salam--Carlitz polynomials
• Generating Functions for Some Families of the Generalized Al-Salam-Carlitz $q$-Polynomials