Definition:Inverse Hyperbolic Cosecant/Real/Definition 1

Definition
The inverse hyperbolic cosecant $\csch^{-1}: \R_{\ne 0} \to \R$ is a real function defined on the non-zero real numbers $\R_{\ne 0}$ as:


 * $\forall x \in \R_{\ne 0}: \map {\csch^{-1} } x := y \in \R: x = \map \csch y$

where $\map \csch y$ denotes the hyperbolic cosecant function of $y$.

Also known as
The inverse hyperbolic cosecant function is also known as the hyperbolic arccosecant function.

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Cosecant