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Wright Type Hypergeometric Function and Its Properties

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Author(s): Snehal B. Rao | Jyotindra C. Prajapati | Ajay K. Shukla

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 03;
Issue: 03;
Start page: 335;
Date: 2013;
Original page

Keywords: Euler Transform | Fox H-Function | Wright Type Hypergeometric Function | Laplace Transform | Mellin Transform | Whittaker Transform | Wright Hypergeometric Function

ABSTRACT
Let s and z be complex variables, Γ(s) be the Gamma function, and   for any complex v be the generalized Pochhammer symbol. Wright Type Hypergeometric Function is defined (Virchenko et al. [1]), as:  where  which is a direct generalization of classical Gauss Hypergeometric Function 2F1(a,b;c;z). The principal aim of this paper is to study the various properties of this Wright type hypergeometric function 2R1(a,b;c;τ;z); which includes differentiation and integration, representation in terms of pFq and in terms of Mellin-Barnes type integral. Euler (Beta) transforms, Laplace transform, Mellin transform, Whittaker transform have also been obtained; along with its relationship with Fox H-function and Wright hypergeometric function.  
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