New Results Involving a Class of Generalized Hurwitz- Lerch Zeta Functions and Their Applications
نویسندگان
چکیده
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada Department of Applied Mathematics, Donghua University, Shanghai, People’s Republic of China Department of Mathematics, M. P. University of Agriculture and Technology, Rajasthan, India *Corresponding author: [email protected] Received September 15, 2013; Revised October 22, 2013; Accepted November 01, 2013 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 Hfunction 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.
منابع مشابه
Geometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function
Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.
متن کاملA New Family of the λ -Generalized Hurwitz-Lerch Zeta Functions with Applications
Abstract: Motivated largely by a number of recent investigations, we introduce and investigate the various properties of a certain new family of the λ -generalized Hurwitz-Lerch zeta functions. We derive many potentially useful results involving these λ -generalized Hurwitz-Lerch zeta functions including (for example) their partial differential equations, new series and Mellin-Barnes type conto...
متن کاملSome properties and results involving the zeta and associated functions
In this research-cum-expository article, we aim at presenting a systematic account of some recent developments involving the Riemann Zeta function ζ(s), the Hurwitz (or generalized) Zeta function ζ(s, a), and the Hurwitz-Lerch Zeta function Φ(z, s, a) as well as its various interesting extensions and generalizations. In particular, we begin by looking into the problems associated with the evalu...
متن کاملHypergeometric Series Associated with the Hurwitz-lerch Zeta Function
The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results.
متن کاملAnother discrete Fourier transform pairs associated with the Lipschitz-Lerch zeta function
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Discrete Fourier transform Alternating zeta functions Hurwitz–Lerch zeta function Lipschitz–Lerch zeta function Le...
متن کامل