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

K.K. Chaudhary; S.B. Rao

doi:10.15421/242402

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

K.K. Chaudhary (The Maharaja Sayajirao University of Baroda), https://orcid.org/0000-0001-7812-1089
S.B. Rao (Maharaja Sayajirao University of Baroda), https://orcid.org/0000-0002-5672-4927

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.

Keywords

basic hypergeometric functions in one variable $$${}_r \phi _s$$$; q-calculus and related topics; Mittag-Leffler functions and generalizations; integral transforms of special functions

MSC 2020

Pri 33D15, Sec 05A30, 33E12, 44A20

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