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http://dx.doi.org/10.4134/BKMS.b190357

EVALUATIONS OF SOME QUADRATIC EULER SUMS  

Si, Xin (School of Applied Mathematics Xiamen University of Technology)
Xu, Ce (School of Mathematical Sciences Xiamen University)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 489-508 More about this Journal
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.
Keywords
Harmonic numbers; polylogarithm function; Euler sum; Riemann zeta function;
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