Symbols:A/Area Hyperbolic Sine/arsinh

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Area Hyperbolic Sine

$\arsinh$


The inverse hyperbolic sine $\arsinh: \R \to \R$ is a real function defined on $\R$ as:

$\forall x \in \R: \map \arsinh x := \map \ln {x + \sqrt {x^2 + 1} }$

where:

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


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


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


Also denoted as

asinh

$\operatorname {asinh}$

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


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