# Definition:Inverse Hyperbolic Tangent/Complex/Principal Branch

## Definition

The principal branch of the complex inverse hyperbolic tangent function is defined as:

$\forall z \in \C: \map \Artanh z := \dfrac 1 2 \, \map \Ln {\dfrac {1 + z} {1 - z} }$

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