Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2013, 1(1), 26-35
DOI: 10.12691/tjant-1-1-7
Open AccessSpecial Issue

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

H. M. Srivastava1, , 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

Pub. Date: November 01, 2013

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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