\begin{definition}[Definition:Inverse Cosecant/Complex/Arccosecant]
The principal branch of the complex inverse cosecant function is defined as:
:$\forall z \in \C_{\ne 0}: \map \arccsc z := \dfrac 1 i \, \map \Ln {\dfrac {i + \sqrt {z^2 - 1} } z}$
where:
:$\Ln$ denotes the principal branch of the complex natural logarithm
:$\sqrt {z^2 - 1}$ denotes the principal square root of $z^2 - 1$.
\end{definition}