Definition:Inverse Hyperbolic Tangent/Complex/Definition 1

Definition
Let $S$ be the subset of the complex plane:
 * $S = \C \setminus \set {-1 + 0 i, 1 + 0 i}$

The inverse hyperbolic tangent is a multifunction defined on $S$ as:


 * $\forall z \in S: \tanh^{-1} \paren z := \set {w \in \C: z = \tanh \paren w}$

where $\tanh \paren w$ is the hyperbolic tangent function.

Also see

 * Equivalence of Definitions of Complex Inverse Hyperbolic Tangent