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