Definition:Inverse Hyperbolic Tangent/Complex/Definition 2

Definition
The inverse hyperbolic tangent is a multifunction defined as:


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

where $\ln$ denotes the complex natural logarithm considered as a multifunction.

Also see

 * Equivalence of Definitions of Inverse Hyperbolic Tangent


 * Definition:Inverse Tangent/Complex/Definition 2