\begin{definition}[Definition:Hyperbolic Cosecant/Definition 2]
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
:$X = \set {z: z \in \C, \ \sinh z \ne 0}$
\end{definition}