Reduction and duality of the generalized Hurwitz-Lerch zetas

Fixexd point theory and applications

Abdelmejid Bayad²  Jamel Chikhi⁶ 

[1] d’DéEssonne, Evry, France;Evry Val d’matiques, Universitépartement de mathé

关键词: Complex Number;    Entire Function;    Analytic Continuation;    Zeta Function;    Series Representation;   

DOI  :  10.1186/1687-1812-2013-82

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, by means of integral representation, we introduce the generalized Hurwitz-Lerch zeta functions of arbitrary complex order. For these functions, we establish the reduction formula and its associated dual formula. We then investigate analytic continuations to the whole complex plane and special values. By means of these reduction and dual formulas, we obtain nice and useful formulas for the Bernoulli-Nörlund and Apostol-Euler-Nörlund polynomials.

【 授权许可】

CC BY