Definition:Inverse Hyperbolic Cotangent/Real/Definition 2

Definition
Let $S$ denote the union of the unbounded open real intervals:
 * $S := \openint \gets {-1} \cup \openint 1 \to$

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


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

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

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Cotangent