A study on unification of generalized hypergeometric function and Mittag-Leffler function with certain integral transforms of generalized basic hypergeometric function

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 generali...

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Bibliographic Details
Published in:	Researches in mathematics (Online) Vol. 32; no. 1; pp. 16 - 32
Main Authors:	Chaudhary, K.K., Rao, S.B.
Format:	Journal Article
Language:	English
Published:	Oles Honchar Dnipro National University 08.07.2024
Subjects:	basic hypergeometric functions in one variable _r \phi _s integral transforms of special functions mittag-leffler functions and generalizations q-calculus and related topics
ISSN:	2664-4991, 2664-5009
Online Access:	Get full text
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Summary:	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:	2664-4991 2664-5009
DOI:	10.15421/242402