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

H. M. Srivastava^1, , Min-Jie Luo² and R. K. Raina³

¹Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

²Department of Applied Mathematics, Donghua University, Shanghai, People’s Republic of China

³Department of Mathematics, M. P. University of Agriculture and Technology, Rajasthan, India

Cite this paper:
H. M. Srivastava, Min-Jie Luo and R. K. Raina. New Results Involving a Class of Generalized Hurwitz-Lerch Zeta Functions and Their Applications. Turkish Journal of Analysis and Number Theory. 2013; 1(1):26-35. doi: 10.12691/tjant-1-1-7

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 H-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.

Keywords:
Hurwitz-Lerch zeta function arithmetic density of number theory partial differential equations series and Mellin-Barnes type contour integral representations Fox’s H-function summation formulas generalized Hurwitz meausure probability density function moment generating function

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