Reduction and duality of the generalized Hurwitz-Lerch zetas

被引：12
|
作者：
Bayad, Abdelmejid [1 ]
Chikhi, Jamel [1 ]
机构：
[1] Univ Evry Val Essonne, Dept Math, F-91037 Evry, France
来源：
FIXED POINT THEORY AND APPLICATIONS | 2013年
关键词：
WEIGHTED STIRLING NUMBERS; BERNOULLI POLYNOMIALS; EULER; EXTENSIONS; PRODUCTS; FORMULAS; SUMS; 1ST;
D O I：
10.1186/1687-1812-2013-82
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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-Norlund and Apostol-Euler-Norlund polynomials.
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页数：14
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