Definition:Inverse Hyperbolic Tangent/Complex/Definition 1

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

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


 * $\forall z \in S: \tanh^{-1} \left({z}\right) := \left\{{w \in \C: z = \tanh \left({w}\right)}\right\}$

where $\tanh \left({w}\right)$ is the hyperbolic tangent function.

Also see

 * Equivalence of Definitions of Complex Inverse Hyperbolic Tangent