A new extension of Hurwitz-Lerch Zeta function

TL;DR

This paper introduces a novel extension of the Hurwitz-Lerch Zeta function using an extended beta function, exploring its properties and special cases to expand its mathematical framework.

Contribution

It presents a new extension of the Hurwitz-Lerch Zeta function and investigates its fundamental properties and special cases.

Findings

Derived integral representations of the extended function

Established differential formulas and Mellin transform relations

Identified special cases with notable properties

Abstract

The main objective of this paper is to introduce a new extension of Hurwitz-Lerch Zeta function in terms of extended beta function. We then investigate its important properties such as integral representations, differential formulas, Mellin transform and certain generating relations. Also, some important special cases of the main results are pointed out.