Certain Identities Involving the General Kampé de Fériet Function and Srivastava’s General Triple Hypergeometric Series

Abstract

Due to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. Among them, the Kampé de Fériet function and its generalizations have been actively researched and applied. The aim of this paper is to provide certain reduction, transformation and summation formulae for the general Kampé de Fériet function and Srivastava’s general triple hypergeometric series, where the parameters and the variables are suitably specified. The identities presented in the theorems and additional comparable outcomes are hoped to be supplied by the use of computer-aid programs, for example, Mathematica. Symmetry occurs naturally in p+1Fp, the Kampé de Fériet function and the Srivastava’s function F(3)[x,y,z], which are three of the most important functions discussed in this study.

Keywords

• Catalan’s constant
• hypergeometric and generalized hypergeometric functions
• Riemann zeta function
• Dirichlet beta function
• (general) Kampé de Fériet function
• Srivastava’s general triple hypergeometric series