Further summation formulas for the Kamp\'e de F\'eriet function

TL;DR

This paper derives thirty-two new summation formulas for the Kampé de Fériet function using advanced identities and generalizations of classical summation theorems, expanding the mathematical toolkit for special functions.

Contribution

It introduces a comprehensive set of new summation formulas for the Kampé de Fériet function, based on generalized identities and classical summation theorems.

Findings

Thirty-two new summation formulas derived

Formulas are expressed in sixteen theorems

Connections with known identities are established

Abstract

The aim of this research is to provide thirty-two interesting summation formulas for the Kamp\'e de F\'eriet function in general forms, which are given in sixteen theorems. The results are established with the help of the identities in Liu and Wang \cite{Li-Wa} and generalizations of Kummer's summation theorem, Gauss' second summation theorem and Bailey's summation theorem obtained earlier by Rakha and Rathie \cite{Ra-Ra}. Some special cases and relevant connections of the results presented here with those involving certain known identities are also indicated.