Mittag-Leffler Expansion for Cosecant Function

Theorem

 * $\displaystyle \pi \csc \pi z = \frac 1 z + 2\sum_{n=1}^\infty \left(-1\right)^n \frac z {z^2 - n^2}$

for non-integer $z \in \C$, where $\csc$ is the cosecant function.