Integral Representation of Riemann Zeta Function in terms of Gamma Function

Theorem
For $\Re \paren s > 1$, the Riemann Zeta function is given by:


 * $\displaystyle \map \zeta s = \frac 1 {\map \Gamma s} \int_0^\infty \frac {t^{s - 1}} {e^t - 1} \rd t$

where $\Gamma$ is the Gamma function.