Definition:Inverse Hyperbolic Secant/Real/Definition 1

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

The inverse hyperbolic secant is a multifunction defined as:


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

where $\operatorname{sech} \left({y}\right)$ denotes the hyperbolic cosine 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