A General Family of $q$-Hypergeometric Polynomials and Associated Generating Functions
| Autor: | Srivastava, Hari Mohan, Arjika, Sama |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Mathematics 9 (11), 1161 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3390/math9111161 |
| Popis: | 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. Comment: 14 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|