\begin{definition}[Definition:Inverse Hyperbolic Cotangent/Complex/Principal Branch]
The principal branch of the complex inverse hyperbolic cotangent function is defined as:
:$\forall z \in \C: \map \Arcoth z := \dfrac 1 2 \map \Ln {\dfrac {z + 1} {z - 1} }$
where $\Ln$ denotes the principal branch of the complex natural logarithm.
\end{definition}