Integral Representation of Riemann Zeta Function in terms of Gamma Function

Theorem
For $\operatorname{Re} \left({s}\right) > 1$, the Riemann Zeta function is given by:


 * $\displaystyle \zeta \left({s}\right) = \frac 1 {\Gamma \left({s}\right)} \int_0^\infty \frac {t^{s - 1}} {e^t - 1} \mathrm d t$

where $\Gamma$ is the Gamma function.