Definition:Inverse Hyperbolic Secant

Real Numbers
Let $S$ denote the half-open real interval:
 * $S := \hointl 0 1$

Hence for $0 < x < 1$, $\map {\sech^{-1} } x$ has $2$ values.

For $x > 0$ and $x > 1$, $\map {\sech^{-1} } x$ is not defined.

Also see

 * Definition:Inverse Hyperbolic Sine
 * Definition:Inverse Hyperbolic Cosine
 * Definition:Inverse Hyperbolic Tangent
 * Definition:Inverse Hyperbolic Cotangent
 * Definition:Inverse Hyperbolic Cosecant