Abstract
In this paper, we provide many new general transformations for multiple hypergeometric functions. These transformations can be viewed as generalizations of some of those obtained recently by Wei et al. (Adv. Differ. Equ. 2013:360, 2013). We obtain these transformations by using the fractional calculus method which is a more general method than the beta integral method.MSC:26A33, 33C20, 33C05.
Highlights
We require two special cases of hypergeometric function of three variables given by Srivastava [ – ]: HA(α, β, β ; γ, γ ; x, y, z) m,n,p≥
The aim of this paper is to present many new general transformations for multiple hypergeometric functions
These transformations can be viewed as generalizations of some of those obtained recently by Wei et al [ ]. All these transformations are obtained by using a fractional calculus operator based on the Pochhammer contour integral
Summary
Other interesting special cases of hypergeometric functions of two variables are Horn’s functions G and G studied in [ , ] and defined as follows: G (α; β , β ; x, y) We require two special cases of hypergeometric function of three variables given by Srivastava [ – ]: HA(α, β , β ; γ , γ ; x, y, z) m,n,p≥ Many authors [ – ] obtained several transformations formulas involving hypergeometric functions as well as their multi-variable analogs by using the so-called beta integral method.
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