\begin{definition}[Definition:Inverse Hyperbolic Tangent/Real/Definition 2]
Let $S$ denote the open real interval:
:$S := \openint {-1} 1$
The '''inverse hyperbolic tangent''' $\artanh: S \to \R$ is a real function defined on $S$ as:
:$\forall x \in S: \map \artanh x := \dfrac 1 2 \map \ln {\dfrac {1 + x} {1 - x} }$
where $\ln$ denotes the natural logarithm of a (strictly positive) real number.
\end{definition}