An elementary proof of some Ramanujan-type identities

TL;DR

This paper provides an elementary proof of identities linking the squares of Riemann zeta function values at integers to series involving hyperbolic functions, digamma functions, and Bernoulli numbers.

Contribution

It introduces a simplified, elementary proof of Ramanujan-type identities for the Riemann zeta function at integers, improving understanding and accessibility.

Findings

Identities expressing zeta squares in terms of hyperbolic series

Elementary proof method for Ramanujan-type identities

Updated and corrected version of previous results

Abstract

We give an elementary proof of some identities that express the squares of Riemann zeta function at integer points in terms of the series involving hyperbolic functions, digamma function, Bernoulli numbers etc. In this version, inaccuracies in the text have been corrected and one of the bibliographic references has been updated.