Definition:Inverse Hyperbolic Tangent/Real/Definition 2

Definition
Let $S$ denote the open real interval:
 * $S := \openint {-1} 1$

The inverse hyperbolic tangent $\tanh^{-1}: S \to \R$ is a real function defined on $S$ as:


 * $\forall x \in S: \map {\tanh^{-1} } x := \dfrac 1 2 \map \ln {\dfrac {1 + x} {1 - x} }$

where $\ln$ denotes the natural logarithm of a (strictly positive) real number.

Also known as
The inverse hyperbolic tangent function is also known as the hyperbolic arctangent function.

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Tangent