An Elementary Proof of Ramanujan's Identity for Odd Zeta Values

TL;DR

This paper provides a simple, elementary proof of Ramanujan's identity for odd zeta values, using basic expansions and classical identities, making the proof more accessible.

Contribution

It introduces an elementary proof of Ramanujan's identity for odd zeta values based on fundamental functions and identities, avoiding complex techniques.

Findings

Elementary proof of Ramanujan's identity for odd zeta values

Relies on Mittag-Leffler expansion and Euler's identity

Simplifies understanding of zeta value relationships

Abstract

The main goal of this article is to present an elementary proof of Ramanujan's identity for odd zeta values. Our proof solely relies on a Mittag-Leffler type expansion for hyperbolic cotangent function and Euler's identity for even zeta values.