Tornheim type series and nonlinear Euler sums

JOURNAL OF NUMBER THEORY

卷:174

Article

Xu, Ce¹  Li, Zhonghua² 

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[2] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

关键词: Tornheim type series;    Harmonic numbers;    Polylogarithm function;    Euler sums;    Riemann zeta function;   

DOI  :  10.1016/j.jnt.2016.10.002

来源: Elsevier

【 摘 要 】

In this paper, we develop an approach to evaluation of non-linear Euler sums. The approach is based on Tornheim type series computations. By the approach, we can obtain some closed form representations of quadratic and cubic sums in terms of zeta values and linear sums. Furthermore, we also evaluate several other series involving harmonic numbers. Some interesting new consequences and illustrative examples are considered. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free