# EVALUATIONS OF SOME QUADRATIC EULER SUMS

• Si, Xin (School of Applied Mathematics Xiamen University of Technology) ;
• Xu, Ce (School of Mathematical Sciences Xiamen University)
• Accepted : 2019.07.04
• Published : 2020.03.31

#### 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 polylogarithms. 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.

#### Acknowledgement

Supported by : National Natural Science Foundation of China, Natural Science Foundation of Fujian Province

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