INTEGRAL REPRESENTATIONS OF EULER-TYPE FOR THE QUADRUPLE HYPERGEOMETRIC FUNCTIONS $F^{(4)}_{20}$

Print ISSN: 2319-1023 | Online ISSN: 2582-5461

Abstract

The authors establish a set of fifteen new integral representations of Euler-type for the Sharma and Parihar hypergeometric function in four variables $F^{(4)}_{20}$; whose kernels include the quadruple functions $K_{1}, K_{10}, F^{(4)}_{14}$ and $X^{(4)}_{8}$; the Exton hypergeometric functions of three variables $X_{4}$; the Lauricella functions of three variable $F_{E}, F_{N}$ and $F_{R}$; the Appell’s series of two variables $F_{2}, F_{3}$ and $F_{4}$; and the Gauss hypergeometric function.

Keywords and Phrases

Beta function, Eulerian integrals, Quadruple hypergeometric series.

A.M.S. subject classification

33C20, 33C65.

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