Some Evaluation of Quadratic Euler Sums

Ce Xu

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arXiv · 1701.03724

Some Evaluation of Quadratic Euler Sums

Ce Xu

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Abstract

In this paper, we obtain some formulas for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. By using these formulas, we give new closed form sums of several quadratic Euler series through Riemann zeta values, polylogarithm functions and linear sums. Furthermore, some relationships between Euler sums and integrals of polylogarithm functions are established.

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Ce Xu. 2017-01-04. Some Evaluation of Quadratic Euler Sums. https://arxiv.org/abs/1701.03724

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