#### Vol. 3, No. 3, 2010

 Recent Issues
 The Journal Cover Page Editorial Board Editors' Addresses Editors' Interests About the Journal Scientific Advantages Submission Guidelines Submission Form Ethics Statement Subscriptions Editorial Login Author Index Coming Soon Contacts ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print)
$\zeta(n)$ via hyperbolic functions

### Joseph D’Avanzo and Nikolai A. Krylov

Vol. 3 (2010), No. 3, 289–296
##### Abstract

We present an approach to compute $\zeta \left(2\right)$ by changing variables in the double integral using hyperbolic trigonometric functions. We also apply this approach to present $\zeta \left(n\right)$, when $n>2$, as a definite improper integral of a single variable.

##### Keywords
multiple integrals, Riemann's zeta function
Primary: 26B15
Secondary: 11M06