Definition:Inverse Hyperbolic Tangent/Real/Definition 1

Definition
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:


 * $\forall x \in S: \map \artanh x := y \in \R: x = \map \tanh y$

where $\map \tanh y$ denotes the hyperbolic tangent function.

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Tangent