Generalized Lerch formulas: Examples of zeta-regularized products

The Lerch zeta function IV. Hecke operators

This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators {Tm : m ≥ 1} given by Tm(f )(a, c) = 1 m ∑m−1 k=0 f ( a+k m ,mc) acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter values. The actions of various related operators on these function spaces are de...

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.

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

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 Nov...

A 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...

Limit Theorem with Weight for Lerch Zeta Function