Definition:Inverse Hyperbolic Tangent/Complex/Principal Branch

Definition
The principal branch of the complex inverse hyperbolic tangent function is defined as:
 * $\forall z \in \C: \operatorname{Tanh}^{-1} \left({z}\right) := \dfrac 1 2 \operatorname{Ln} \left({\dfrac {1 + z} {1 - z} }\right)$

where $\operatorname{Ln}$ denotes the principal branch of the complex natural logarithm.

Also see

 * Derivation of Hyperbolic Arctangent from Inverse Hyperbolic Tangent Multifunction