A New Family of the λ -Generalized Hurwitz-Lerch Zeta Functions with Applications

Authors

H. M. Srivastava, Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, CanadaFollow

Author Country (or Countries)

Canada

Abstract

Motivated largely by a number of recent investigations, we introduce and investigate the various properties of a certain new family of the l -generalized Hurwitz-Lerch zeta functions. We derive many potentially useful results involving these l -generalized Hurwitz-Lerch zeta functions including (for example) their partial differential equations, new series and Mellin-Barnes type contour integral representations (which are associated with Fox’s H-function) and several other summation formulas.We discuss their potential application in Number Theory by appropriately constructing a seemingly novel continuous analogue of Lippert’s Hurwitz measure. We also consider some other statistical applications of the family of the l -generalized Hurwitz-Lerch zeta functions in probability distribution theory.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/080402

Recommended Citation

M. Srivastava, H. (2014) "A New Family of the λ -Generalized Hurwitz-Lerch Zeta Functions with Applications," Applied Mathematics & Information Sciences: Vol. 08: Iss. 4, Article 2.
DOI: http://dx.doi.org/10.12785/amis/080402
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss4/2