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

Hari Mohan Srivastava and Sama Arjika
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Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Sama Arjika: Department of Mathematics and Informatics, University of Agadez, P.O. Box 199, Agadez 8000, Niger

Mathematics, 2021, vol. 9, issue 11, 1-15

Abstract: Basic (or q -) series and basic (or q -) polynomials, especially the basic (or q -) hypergeometric functions and the basic (or q -) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, 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.

Keywords: basic (or q -) hypergeometric series; homogeneous q -difference operator; q -binomial theorem; cauchy polynomials; Al-Salam-Carlitz q -polynomials; rogers type formulas; Srivastava-Agarwal type generating functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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