On a new class of series identities

TL;DR

This paper introduces a new class of series identities derived from generalized Kummer's summation theorem, unifying and extending previous results by Srivastava, Bailey, and Rathie.

Contribution

It presents four general series identities based on generalized Kummer's theorem, expanding the scope of existing series summation formulas.

Findings

Four general series identities established

Extensions of classical Kummer's theorem demonstrated

Previous results are special cases of the new identities

Abstract

The aim of this paper is to provide a new class of series identities in the form of four general results. The results are established with the help of generalizatons of the classical Kummer's summation theorem obtained earlier by Rakha and Rathie. Results obtained earlier by Srivastava, Bailey and Rathie et al. follow special cases of our main findings.