A study on unification of generalized hypergeometric function and Mittag-Leffler function with certain integral transforms of generalized basic hypergeometric function
Saved in:
| Title: | A study on unification of generalized hypergeometric function and Mittag-Leffler function with certain integral transforms of generalized basic hypergeometric function |
|---|---|
| Authors: | K.K. Chaudhary, S.B. Rao |
| Source: | Researches in Mathematics, Vol 32, Iss 1, Pp 16-32 (2024) |
| Publisher Information: | Oles Honchar Dnipro National University, 2024. |
| Publication Year: | 2024 |
| Collection: | LCC:Mathematics |
| Subject Terms: | basic hypergeometric functions in one variable ${}_r \phi _s$, q-calculus and related topics, mittag-leffler functions and generalizations, integral transforms of special functions, Mathematics, QA1-939 |
| Description: | This research article explores some new properties of generalized hypergeometric function and its q-analogue. The connections between ${}_{2}{{R}_{1}}^{\upsilon }(\mathfrak{z})$, the Wright function, and generalized Mittag-Leffler functions are explored. The authors introduce the q-analogue of generalized hypergeometric function denoted by ${}_{2}{{R}_{1}}^{\upsilon ,q}(\mathfrak{z})$ and discuss its properties and connections with q-Wright function and q-versions of generalized Mittag-Leffler functions. We get the q-integral transforms such as q-Mellin, q-Euler (beta), q-Laplace, q-sumudu, and q-natural transforms of Wright-type generalized q-hypergeometric function. This article contributes to the understanding of hypergeometric functions in q-calculus. |
| Document Type: | article |
| File Description: | electronic resource |
| Language: | English |
| ISSN: | 2664-4991 2664-5009 |
| Relation: | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/414/414; https://doaj.org/toc/2664-4991; https://doaj.org/toc/2664-5009 |
| DOI: | 10.15421/242402 |
| Access URL: | https://doaj.org/article/4b9b8853aaa84d39b7cffa4f76f6b8e6 |
| Accession Number: | edsdoj.4b9b8853aaa84d39b7cffa4f76f6b8e6 |
| Database: | Directory of Open Access Journals |
Nájsť tento článok vo Web of Science | Abstract: | This research article explores some new properties of generalized hypergeometric function and its q-analogue. The connections between ${}_{2}{{R}_{1}}^{\upsilon }(\mathfrak{z})$, the Wright function, and generalized Mittag-Leffler functions are explored. The authors introduce the q-analogue of generalized hypergeometric function denoted by ${}_{2}{{R}_{1}}^{\upsilon ,q}(\mathfrak{z})$ and discuss its properties and connections with q-Wright function and q-versions of generalized Mittag-Leffler functions. We get the q-integral transforms such as q-Mellin, q-Euler (beta), q-Laplace, q-sumudu, and q-natural transforms of Wright-type generalized q-hypergeometric function. This article contributes to the understanding of hypergeometric functions in q-calculus. |
|---|---|
| ISSN: | 26644991 26645009 |
| DOI: | 10.15421/242402 |