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

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 t...

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Published in:Mathematics (Basel) Vol. 9; no. 11; p. 1161
Main Authors: Srivastava, Hari Mohan, Arjika, Sama
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.06.2021
Subjects:
Al-Salam-Carlitz q-polynomials
basic (or q-) hypergeometric series
cauchy polynomials
homogeneous q-difference operator
Hypergeometric functions
Identities
Investigations
Mathematical analysis
Physical sciences
Polynomials
q-binomial theorem
rogers type formulas
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9111161