TITLE:
Wright Type Hypergeometric Function and Its Properties
AUTHORS:
Snehal B. Rao, Jyotindra C. Prajapati, Ajay K. Shukla
KEYWORDS:
Euler Transform; Fox H-Function; Wright Type Hypergeometric Function; Laplace Transform; Mellin Transform; Whittaker Transform; Wright Hypergeometric Function
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.3,
May
13,
2013
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.