Generalized q-difference equations for q-hypergeometric polynomials with double q-binomial coefficients
Date
2022
Authors
Cao, Jian
Srivastava, H.M.
Zhou, Hong-Li
Arjika, Sama
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
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.
Description
Keywords
homogeneous q-difference operator, double q-binomial coefficients, q-difference equations, q-hypergeometric polynomials, generating functions
Citation
Cao, J., Srivastava, H., Zhou, H., & Arjika, S. (2022). “Generalized q-difference equations for q-hypergeometric polynomials with double q-binomial coefficients.” Mathematics, 10(4), 556. https://doi.org/10.3390/math10040556