Mittag-Leffler Expansion for Cotangent Function

Theorem

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

where:
 * $z \in \C$ is not an integer
 * $\cot$ is the cotangent function.

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