Wright Type Hypergeometric Function and Its Properties
- 1 Department of Applied Mathematics, The M.S. University of Baroda, Vadodara, India
- 2 Department of Mathematical Sciences, Faculty of Applied Sciences, Charotar University of Science and Technology, Anand, India
- 3 Department of Applied Mathematics and Humenities, S.V. National Institute of Technology, Surat, India
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 2 F 1 ( a , b ; c ; z ) . The principal aim of this paper is to study the various properties of this Wright type hypergeometric function 2 R 1 ( a , b ; c ; τ ; z ) ; which includes differentiation and integration, representation in terms of p F q 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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