A General Family of $q$-Hypergeometric Polynomials and Associated Generating Functions
Hari Mohan Srivastava, Sama Arjika

TL;DR
This paper introduces a broad family of $q$-hypergeometric polynomials, explores their generating functions and identities, and connects these results with existing literature, highlighting the redundancy of $(p,q)$-variations.
Contribution
It presents a new general family of $q$-hypergeometric polynomials and derives several novel generating function identities and transformational relations.
Findings
Extended generating functions for the new family
Bilinear generating functions of Srivastava-Agarwal type
Connections with previous $q$-series results
Abstract
In this paper, we introduce a general family of -hypergeometric polynomials and investigate several -series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of -hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized -hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various -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 -variations of the -results, which we have investigated here, because the additional parameter is obviously redundant.
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