Extension of a summation due to Ramanujan

TL;DR

This paper extends a classical summation formula originally discovered by Ramanujan, utilizing an extended version of Gauss's summation theorem to derive new mathematical identities.

Contribution

It introduces a novel extension of Ramanujan's summation formula based on an existing generalization of Gauss's theorem.

Findings

Derived a new summation extension related to Ramanujan's work

Utilized an extended form of Gauss's summation theorem

Provided mathematical identities expanding classical summation formulas

Abstract

In this short research note, we aim to establish an interesting extension of a summation due to Ramanujan.The result is derived with the help of an extension of Gauss's summation theorem available in the literature.