# Definition:Hyperbolic Cosecant/Definition 2

## Definition

The hyperbolic cosecant function is defined on the complex numbers as:

$\csch: X \to \C$:
$\forall z \in X: \csch z := \dfrac 1 {\sinh z}$

where:

$\sinh$ is the hyperbolic sine
$X = \set {z : z \in \C, \ \sinh z \ne 0}$