Mittag-Leffler Expansion for Hyperbolic Cosecant Function

Theorem

 * $\displaystyle \pi \csch \paren {\pi z} = \frac 1 z + 2 \sum_{n \mathop = 1}^\infty \paren {-1}^n \frac z {z^2 + n^2}$

where:
 * $z \in \C$ is not an integer multiple of $i$
 * $\csch$ is the hyperbolic cosecant function.