Hurwitz Zeta Functions and Ramanujan's Identity for Odd Zeta Values

TL;DR

This paper generalizes Ramanujan's identity for odd zeta values by deriving analogous formulas involving the Hurwitz zeta function and introducing a new integral kernel.

Contribution

It introduces a new integral kernel related to the Hurwitz zeta function and generalizes Ramanujan's identity to a broader class of functions.

Findings

Derived an analogous formula involving the Hurwitz zeta function

Introduced a new integral kernel related to Hurwitz zeta

Established infinite families of identities similar to Ramanujan's

Abstract

Inspired by a famous formula of Ramanujan for odd zeta values, we prove an analogous formula involving the Hurwitz zeta function. We introduce a new integral kernel related to the Hurwitz zeta function, generalizing the integral kernel associated to Ramanujan's identity. We also derive several infinite families of identities analogous to Ramanujan's formula.