$\zeta(n)$ via hyperbolic functions

Joseph D’Avanzo; Nikolai Krylov

doi:10.2140/involve.2010.3.289

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Home > Journals > Involve > Volume 3 > Issue 3 > Article

2010 $\zeta(n)$ via hyperbolic functions

Joseph D’Avanzo, Nikolai Krylov

Involve 3(3): 289-296 (2010). DOI: 10.2140/involve.2010.3.289

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Abstract

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