Mittag-Leffler Expansion for Cosecant Function

Theorem

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

where:
 * $z \in \C$ is not an integer
 * $\cosec$ is the cosecant function.

Real Domain
Let $\alpha \in \R$ be a real number which is specifically not an integer.

Then: