Symbols:A/Area Hyperbolic Cosine
Area Hyperbolic Cosine
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 $\map \arcosh x \ge 0$.
arcosh
- $\arcosh$
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 .
acosh
- $\operatorname {acosh}$
A variant symbol used to denote the area hyperbolic cosine function is $\operatorname {acosh}$.
Its $\LaTeX$ code is \operatorname {acosh} .
arccosh
- $\operatorname {arccosh}$
A questionable symbol used to denote the area hyperbolic cosine function is $\operatorname {arccosh}$.
Its $\LaTeX$ code is \operatorname {arccosh} .
arc cosh
- $\operatorname {arc cosh}$
A questionable and clumsy symbol used to denote the area hyperbolic cosine function is $\operatorname {arc cosh}$.
Its $\LaTeX$ code is \operatorname {arc cosh} .