\begin{definition}[Definition:Inverse Hyperbolic Cosecant/Complex/Definition 1]
The '''inverse hyperbolic cosecant''' is a multifunction defined as:
:$\forall z \in \C_{\ne 0}: \map {\csch^{-1} } z := \set {w \in \C: z = \map \csch w}$
where $\map \csch w$ is the hyperbolic cosecant function.
\end{definition}