A study on unification of generalized hypergeometric function and Mittag-Leffler function with certain integral transforms of generalized basic hypergeometric function
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| Titel: | A study on unification of generalized hypergeometric function and Mittag-Leffler function with certain integral transforms of generalized basic hypergeometric function |
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| Autoren: | K.K. Chaudhary, S.B. Rao |
| Quelle: | Researches in Mathematics, Vol 32, Iss 1, Pp 16-32 (2024) |
| Verlagsinformationen: | Oles Honchar Dnipro National University, 2024. |
| Publikationsjahr: | 2024 |
| Bestand: | LCC:Mathematics |
| Schlagwörter: | 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 |
| Beschreibung: | 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. |
| Publikationsart: | article |
| Dateibeschreibung: | electronic resource |
| Sprache: | 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 |
| Zugangs-URL: | https://doaj.org/article/4b9b8853aaa84d39b7cffa4f76f6b8e6 |
| Dokumentencode: | edsdoj.4b9b8853aaa84d39b7cffa4f76f6b8e6 |
| Datenbank: | 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. |
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| ISSN: | 26644991 26645009 |
| DOI: | 10.15421/242402 |