New Results Involving a Class of Generalized Hurwitz-Lerch Zeta Functions and Their Applications

Abstract

In this paper, we study a certain class of generalized Hurwitz-Lerch zeta functions. We derive several new and useful properties of these generalized Hurwitz-Lerch zeta functions such as (for example) their partial differential equations, new series and Mellin-Barnes type contour integral representations involving Fox’s <i>H</i>-function and a pair of summation formulas. More importantly, by considering their application in Number Theory, we construct a new continuous analogue of Lippert’s Hurwitz measure. Some statistical applications are also given.