English

Zeta(n) via hyperbolic functions

Classical Analysis and ODEs 2010-11-03 v2

Abstract

We present here an approach to a computation of ζ(2)\zeta(2) by changing variables in the double integral using hyperbolic trig functions. We also apply this approach to present ζ(n)\zeta(n), when n>2n>2, as a definite improper integral of single variable.

Keywords

Cite

@article{arxiv.1007.3436,
  title  = {Zeta(n) via hyperbolic functions},
  author = {Joseph T. D'Avanzo and Nikolai A. Krylov},
  journal= {arXiv preprint arXiv:1007.3436},
  year   = {2010}
}

Comments

10 pages, 1 figure, to be published in Involve, a Journal of Mathematics. A recent paper was added to the reference list

R2 v1 2026-06-21T15:50:29.175Z