Explicit evaluation of quadratic Euler sums

Ce Xu; Yingyue Yang; Jianwen Zhang

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arXiv · 1609.04923

Explicit evaluation of quadratic Euler sums

Ce Xu·Yingyue Yang·Jianwen Zhang

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Abstract

In this paper, we work out some explicit formulae for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. As applications of these formulae, we give new closed form representations of several quadratic Euler sums through Riemann zeta function and linear sums. The given representations are new.

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Ce Xu, Yingyue Yang, Jianwen Zhang. 2016-09-16. Explicit evaluation of quadratic Euler sums. https://arxiv.org/abs/1609.04923

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