Abstract

The aim of the present paper is to further study the S-generalized Gauss hypergeometric function transform recently introduced by Srivastava, Jain and Bansal [11]. In the course of our study, we establish image of Fox H-function in the S-Generalized Gauss hypergeometric function transform and obtain the images of five useful and important cases of Fox H-function (Generalized Bessel function, Gauss Hypergeometric function, Generalized Mittag-Leffler Function, Kr¨atzel Function and Lorenzo Hartley G-function) under the S-generalized Gauss hypergeometric function transform.

Keywords and Phrases

S-Generalized Gauss hypergeometric function, Fox H-Function, Complex integral representation, Integral transform.

A.M.S. subject classification

33C20; 33C60; 30E20; 44A20.

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