Integral using the Hyperbolic Sine

Click on the image for a detailed proof

\zeta(s)=\frac{2^{s-1}}{\Gamma(s+1)}\int_{0}^{\infty}\frac{x^s}{\sinh(x)^2}dx

This is one of the first discovered Formulas linking the Riemann Zeta and the Hyperbolic sine.

The demonstration we explain is based on the Relation to the Gamma Function 1.

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