Evaluations of some quadratic Euler sums
Number Theory
2017-03-28 v2
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.
Cite
@article{arxiv.1701.00389,
title = {Evaluations of some quadratic Euler sums},
author = {Xin Si and Ce Xu},
journal= {arXiv preprint arXiv:1701.00389},
year = {2017}
}