The evaluation of Tomheim double sums, Part 1

被引：34

作者：

Espinosa, O

Moll, VH ^{[1
]}

机构：

[1] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

[2] Univ Tecn Federico Santa Maria, Dept Fis, Valparaiso, Chile

来源：

JOURNAL OF NUMBER THEORY | 2006年 / 116卷 / 01期

关键词：

Hurwitz zeta function;

D O I：

10.1016/j.jnt.2005.04.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide an explicit formula for the Tornheim double series in terms of integrals involving the Hurwitz zeta function. We also study the limit when the parameters of the Tornheim sum become natural numbers, and show that in that case it can be expressed in terms of definite integrals of triple products of Bernoulli polynomials and the Bernoulli function A(k)(q) k zeta'(1-k, q). (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：200 / 229

页数：30

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