Definition:Inverse Hyperbolic Tangent/Complex/Principal Branch

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

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

Also see

 * Derivation of Hyperbolic Arctangent from Inverse Hyperbolic Tangent Multifunction