Wright Type Hypergeometric Function and Its Properties

• 作者: Ajay K. Shukla Jyotindra C. Prajapati Snehal B. Rao
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: Euler TRANSFORM Fox H-FUNCTION WRIGHT TYPE HYPERGEOMETRIC FUNCTION Laplace TRANSFORM Mellin TRANSFORM Whittaker TRANSFORM WRIGHT HYPERGEOMETRIC FUNCTION
• 年，卷（期）: 2013,（3）
• 页码范围: 335-342
• 页数: 8页
• 分类号: O1

摘要

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.