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

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dc.contributor.authorSrivastava, H.M.
dc.contributor.authorArjika, Sama
dc.date.accessioned2021-06-27T14:55:54Z
dc.date.available2021-06-27T14:55:54Z
dc.date.copyright2021en_US
dc.date.issued2021
dc.description.abstractBasic (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.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.identifier.citationSrivastava, H. M. & Arjika, S. (2021). A General Family of q-Hypergeometric Polynomials and Associated Generating Functions. Mathematics, 9(11), 1-15. https://doi.org/10.3390/math9111161.en_US
dc.identifier.urihttps://doi.org/10.3390/math9111161
dc.identifier.urihttp://hdl.handle.net/1828/13075
dc.language.isoenen_US
dc.publisherMathematicsen_US
dc.subjectbasic (or q-) hypergeometric series
dc.subjecthomogeneous q-difference operator
dc.subjectq-binomial theorem
dc.subjectcauchy polynomials
dc.subjectAl-Salam-Carlitz q-polynomials
dc.subjectrogers type formulas
dc.subjectSrivastava-Agarwal type generating functions
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleA General Family of q-Hypergeometric Polynomials and Associated Generating Functionsen_US
dc.typeArticleen_US

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