Definition:Inverse Hyperbolic Secant/Real/Definition 2

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

The inverse hyperbolic secant $\arsech S \to \R$ is a real function defined on $S$ as:


 * $\forall x \in S: \map \arsech x := \map \ln {\dfrac {1 + \sqrt {1 - x^2} } x}$

where:
 * $\ln$ denotes the natural logarithm of a (strictly positive) real number.
 * $\sqrt {1 - x^2}$ denotes the positive square root of $1 - x^2$

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Secant