Definition:Inverse Hyperbolic Tangent/Complex/Definition 2

Definition
The inverse hyperbolic tangent is a multifunction defined as:


 * $\forall z \in \C: \tanh^{-1} \left({z}\right) := \dfrac 1 2 \ln \left({\dfrac {1 + z} {1 - z} }\right)$

where $\ln$ is the complex natural logarithm function.

As $\ln$ is a multifunction it follows that $\tanh^{-1}$ is likewise a multifunction.

Also see

 * Equivalence of Definitions of Inverse Hyperbolic Tangent