English

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.

Keywords

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

R2 v1 2026-06-22T17:49:42.923Z