Further Novel reductions of Kamp\'e de F\'eriet function

TL;DR

This paper introduces twenty-four new reduction formulas for Kampé de Fériet functions, expanding the mathematical tools available for simplifying complex hypergeometric functions using Beta and Gamma integrals.

Contribution

It provides novel reduction formulas for Kampé de Fériet functions, building upon previous identities and applying integral methods to derive these new results.

Findings

Twenty-four new reduction formulas derived.

Application of Beta and Gamma integrals to hypergeometric functions.

Extension of previous work by Rathie, Pogany, Kim, and Rathie.

Abstract

In a recent paper, Rathie and Pogany established thirty two novel and general reductions of two and three variables generalized hypergeometric functions. In this paper we provide twenty four further novel and general reduction formulas. The results are established by the application of Beta and Gamma integral methods to the three identities involving products of generalized hypergeometric functions obtained earlier by Kim and Rathie. As special cases, we mention some interesting results.