Mittag-Leffler Expansion for Hyperbolic Tangent Function

Theorem

 * $\displaystyle \pi \tanh \paren {\pi z} = 8 \sum_{n \mathop = 0}^\infty \frac z {4 z^2 + \paren {2 n + 1}^2}$

where:
 * $z \in \C$ is not a half-integer multiple of $i$
 * $\tanh$ is the hyperbolic tangent function.