Hankel Representation of Riemann Zeta Function

Theorem
Let $C$ be the Hankel contour.

Then for $s \in \C \setminus \Z_{>0}$:


 * $\ds \map \zeta s = \frac {i \Gamma \paren {1 - s} } {2 \pi} \oint_C \frac {\paren {-z}^{s - 1} } {e^z - 1} \rd z$

where:
 * $\zeta$ is the Riemann Zeta function
 * $\Gamma$ is the Gamma function.