Symbols:A/Area Hyperbolic Secant/arsech

Area Hyperbolic Secant

$\arsech$

The principal branch of the real inverse hyperbolic secant function is defined 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.

$\sqrt {1 - x^2}$ specifically denotes the positive square root of $x^2 - 1$

That is, where $\map \arsech x \ge 0$.

The usual symbol used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to denote the area hyperbolic secant function is $\arsech$.

The $\LaTeX$ code for \(\arsech\) is \arsech .

Also denoted as

asech

$\operatorname {asech}$

A variant symbol used to denote the area hyperbolic secant function is $\operatorname {asech}$.

The $\LaTeX$ code for \(\operatorname {asech}\) is \operatorname {asech} .