Definition:Inverse Hyperbolic Cosecant/Real/Definition 1

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


 * $\forall x \in \R_{\ne 0}: \operatorname{csch}^{-1} \left({x}\right) = \left\{{y \in \R: x = \operatorname{csch} \left({y}\right)}\right\}$

where $\operatorname{csch} \left({y}\right)$ denotes the hyperbolic cosecant function.

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