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

Author

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  • Hari Mohan Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ 1007, Azerbaijan
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy)

  • Sama Arjika

    (Department of Mathematics and Informatics, University of Agadez, P.O. Box 199, Agadez 8000, Niger)

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.

Suggested Citation

  • Hari Mohan Srivastava & Sama Arjika, 2021. "A General Family of q -Hypergeometric Polynomials and Associated Generating Functions," Mathematics, MDPI, vol. 9(11), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1161-:d:559229
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