\begin{definition}[Definition:Hyperbolic Cosecant/Definition 1]
The '''hyperbolic cosecant''' function is defined on the complex numbers as:
:$\csch: X \to \C$:
:$\forall z \in X: \csch z := \dfrac 2 {e^z - e^{-z} }$
where:
: $X = \set {z: z \in \C, \ e^z - e^{-z} \ne 0}$
\end{definition}