Tornheim type series and nonlinear Euler sums

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• 作者：Ce Xu^a ; ^{15959259051@163.com} ; Zhonghua Li^b ; ^{zhonghuali@tongji.edu.cn}
• 关键词：11M06 ; 11M32 ; 33B99 ; 33E20 ; 40A05
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：174
• 期：Complete
• 页码：40-67
• 全文大小：406 K
• 卷排序：174

文摘

In this paper, we develop an approach to evaluation of nonlinear 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.