Definition:Inverse Hyperbolic Cotangent/Real/Definition 1

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

The inverse hyperbolic cotangent $\arcoth: S \to \R$ is a real function defined on $S$ as:


 * $\forall x \in S: \arcoth x := y \in \R: x = \coth y$

where $\coth y$ denotes the hyperbolic cotangent function.

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Cotangent