Definition:Inverse Hyperbolic Secant/Real/Definition 1

Definition
Let $S$ denote the half-open real interval:
 * $S := \left({0 \,.\,.\, 1}\right]$

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


 * $\forall x \in S: \operatorname{sech}^{-1} \left({x}\right) := y \in \R_{\ge 0}: x = \operatorname{sech} \left({y}\right)$

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

Also known as
The inverse hyperbolic secant function is also known as the hyperbolic arcsecant function.

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Secant