Symbols:A/Area Hyperbolic Cosine/arcosh

Area Hyperbolic Cosine

$\arcosh$

The principal branch of the real inverse hyperbolic cosine function is defined as:

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

where:

$\ln$ denotes the natural logarithm of a (strictly positive) real number.

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

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

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

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

Also denoted as

acosh

$\operatorname {acosh}$

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

Its $\LaTeX$ code is \operatorname {acosh} .