Evaluations of some quadratic Euler sums

Xin Si; Ce Xu

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arXiv · 1701.00389

Evaluations of some quadratic Euler sums

Xin Si·Ce Xu

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Abstract

This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polyloga- rithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.

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BibTeX RIS

Xin Si, Ce Xu. 2017-01-02. Evaluations of some quadratic Euler sums. https://arxiv.org/abs/1701.00389

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