Quadratic and cubic harmonic number sums

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• 作者：Xin Si^a ; ^{xsi@xmut.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Ce Xu^b ; ^{15959259051@163.com" class="auth_mail" title="E-mail the corresponding author} ; Mingyu Zhang^b ; ^{zhangmingyubaobao@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Polylogarithm function ; Euler sums ; Riemann zeta function ; Harmonic numbers
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：419-434
• 全文大小：328 K

文摘

This paper develops an approach to evaluation of Euler related sums. The approach is based on simple integral computations. By the approach, we can obtain some closed form representations of sums of quadratic and cubic harmonic numbers and reciprocal binomial coefficients. The given representations are new.