Mittag-Leffler Expansion for Hyperbolic Secant Function

Theorem

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

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