On a Certain Extension of the Hurwitz-Lerch Zeta Function

Abstract

Our purpose in this paper is to consider a generalized form of the extended Hurwitz-Lerch Zeta function. For this extended Hurwitz-Lerch Zeta function, we obtain some classical properties which includes various integral representations, a differential formula, Mellin transforms and certain generating relations. We further consider an application to probability distributions and also point out some important special cases of the main results.

Keywords

• generalized hurwitz-lerch zeta function
• extended beta function
• extended hypergeometric function
• extended hurwitz-lerch zeta function
• mellin transform
• probability density function