Mittag-Leffler Expansion for Hyperbolic Tangent Function

From ProofWiki
Jump to navigation Jump to search

Theorem

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

where:

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


Proof




Source of Name

This entry was named for Magnus Gustaf Mittag-Leffler.


Sources