English

On some series formed by values of the Riemann Zeta function

Complex Variables 2015-11-17 v1 Number Theory

Abstract

The partial fraction expansion of coth(π\piz), due to Euler, is generalized to power series having for coefficients the Riemann zeta function evaluated at certain arithmetic sequences. A further generalization using arbitrary Dirichlet series is also proposed. The resulting formulas are new, as far as we know, since they could not be found in any of the classical or recent handbooks of formulas that were at our disposal.

Keywords

Cite

@article{arxiv.1511.04720,
  title  = {On some series formed by values of the Riemann Zeta function},
  author = {Claude Henri Picard},
  journal= {arXiv preprint arXiv:1511.04720},
  year   = {2015}
}