Symbols:A/Area Hyperbolic Sine/asinh

Area Hyperbolic Sine

$\operatorname {asinh}$

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 $x^2 + 1$.

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

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

Also denoted as

arsinh

$\arsinh$

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 .

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): asinh