A note on the Hurwitz-Lerch zeta function

TL;DR

This paper derives a functional equation and definite integrals involving the Hurwitz-Lerch zeta function using contour integration, providing special cases related to fundamental constants.

Contribution

It introduces new functional equations and integral formulas for the Hurwitz-Lerch zeta function using contour integration methods.

Findings

Derived a functional equation for the Hurwitz-Lerch zeta function.

Established definite integrals involving incomplete gamma and Hurwitz-Lerch zeta functions.

Produced special cases related to fundamental constants.

Abstract

In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour integration. Special cases in terms of fundamental constants are produced.