EXTENDED GENERALIZED $\tau$-GAUSS' HYPERGEOMETRIC FUNCTIONS AND THEIR APPLICATIONS

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 311

Volume : 18 , Issue : 3
DOI: https://doi.org/10.56827/SEAJMMS.2022.1803.6
Author :
Bharti Chauhan (Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida - 201301, Uttar Pradesh, INDIA)
Prakriti Rai (Department of Mathematics, Siddharth University, Kapilvastu, (U. P.), INDIA)

Abstract

In this article, by means of the extended beta function, we introduce new extension of the generalized $\tau$-Gauss' hypergeometric functions and present some new integral and series representations (including the one obtained by adopting the well-known Ramanujan's Master Theorem). We also consider some new and known results as consequences of our proposed extension of the generalized $\tau$-Gauss hypergeometric function.

Keywords and Phrases

Extended Beta function, Generalized $\tau$-Gauss' hypergeometric function, Ramanujan's Master theorem.

A.M.S. subject classification

33B15, 33B20, 33C20, 33D05.

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