New identities for the family of Zeta function by using distributional representations

TL;DR

This paper derives new identities for the Riemann zeta function, its related functions, and the gamma function using distributional representations, expanding the analytical tools available for studying these fundamental functions.

Contribution

It introduces novel identities for the Riemann zeta, Dirichlet eta, and Lambda functions based on distributional representations, extending previous gamma function results.

Findings

New identities for the Riemann zeta function

Identities involving Dirichlet eta and Lambda functions

Extension of distributional representation techniques

Abstract

Chaudhry and Qadir obtained new identities for the gamma function by using a distributional representation for it. Here we obtain new identities for the Riemann zeta function and its family by using that representation for them. This also leads to new identities involving the Dirichlet eta and Lambda functions.