Vol. 3, No. 3, 2010

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$\zeta(n)$ 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