Notes on a paper of Tyagi and Holm: A new integral representation for the Riemann Zeta function

TL;DR

This paper discusses a new series representation of the Riemann Zeta function introduced by Tyagi and Holm, which yields novel recursions for Bernoulli numbers and new series involving Zeta functions at integer points.

Contribution

It introduces a new integral series representation of the Riemann Zeta function that leads to fresh recursive formulas for Bernoulli numbers and new series representations.

Findings

New recursion formulas for Bernoulli numbers of even index

Novel series representations involving Zeta functions at integers

Enhanced understanding of the structure of the Riemann Zeta function

Abstract

It is shown that a new series representation of Riemann s Zeta function obtained by Tyagi and Holm leads to an interesting new recursion for Bernoulli numbers of even index as well as new representations of, and infinite series involving, Zeta functions of special (integer) argument.