Generalization of some of Ramanujan's formulae

TL;DR

This paper uses partial fractions to generalize Ramanujan's infinite series identities, including those for zeta(2n+1), and extends the transformation formula for the Dedekind eta function, revealing broader applicability of the method.

Contribution

It introduces a novel application of partial fractions to generalize classical Ramanujan formulas and Dedekind eta transformations.

Findings

Generalized Ramanujan's series identities

Extended the transformation formula for Dedekind eta

Demonstrated broad applicability of partial fractions

Abstract

We shall make use of the method of partial fractions to generalize some of Ramanujan's infinite series identities, including Ramanujan's famous formula for $\zeta(2n+1)$, and we shall also give a generalization of the transformation formula for the Dedekind eta function. It is shown here that the method of partial fractions can be used to obtain many similar identities of this kind.