Evaluations of some quadratic Euler sums
Bull. Korean Math. Soc.
Published online August 2, 2019
Xin Si and Ce Xu
School of Applied Mathematics, Xiamen University of Technology, School of Mathematical Sciences, Xiamen University
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.
Keywords : Harmonic numbers; polylogarithm function; Euler sum; Riemann zeta function.
MSC numbers : 11M06; 11M32; 33B15
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