Generalized q -Difference Equations for q -Hypergeometric Polynomials with Double q -Binomial Coefficients

Jian Cao, Hari M. Srivastava, Hong-Li Zhou and Sama Arjika
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Jian Cao: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Hari M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Hong-Li Zhou: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Sama Arjika: Department of Mathematics and Informatics, University of Agadez, Agadez P.O. Box 199, Niger

Mathematics, 2022, vol. 10, issue 4, 1-17

Abstract: In this paper, we apply a general family of basic (or q -) polynomials with double q -binomial coefficients as well as some homogeneous q -operators in order to construct several q -difference equations involving seven variables. We derive the Rogers type and the extended Rogers type formulas as well as the Srivastava-Agarwal-type bilinear generating functions for the general q -polynomials, which generalize the generating functions for the Cigler polynomials. We also derive a class of mixed generating functions by means of the aforementioned q -difference equations. The various results, which we have derived in this paper, are new and sufficiently general in character. Moreover, the generating functions presented here are potentially applicable not only in the study of the general q -polynomials, which they have generated, but indeed also in finding solutions of the associated q -difference equations. Finally, we remark that it will be a rather trivial and inconsequential exercise to produce the so-called ( p , q ) -variations of the q -results, which we have investigated here, because the additional forced-in parameter p is obviously redundant.

Keywords: homogeneous q -difference operator; double q -binomial coefficients; q -difference equations; q -hypergeometric polynomials; generating functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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