Mittag-Leffler Expansion for Square of Secant Function

Theorem

 * $\ds \pi^2 \map {\sec^2} {\pi z} = 8 \sum_{n \mathop = 0}^\infty \frac {\paren {2 n + 1} + 4 z^2} {\paren {\paren {2 n + 1}^2 - 4 z^2}^2}$

where:
 * $z$ is a complex number that is not a half-integer
 * $\sec$ denotes the secant function.