Some Evaluation of Quadratic Euler Sums
Number Theory
2017-01-16 v1
Abstract
In this paper, we obtain some formulas for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. By using these formulas, we give new closed form sums of several quadratic Euler series through Riemann zeta values, polylogarithm functions and linear sums. Furthermore, some relationships between Euler sums and integrals of polylogarithm functions are established.
Cite
@article{arxiv.1701.03724,
title = {Some Evaluation of Quadratic Euler Sums},
author = {Ce Xu},
journal= {arXiv preprint arXiv:1701.03724},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1701.00388