Symbols:A/Area Hyperbolic Sine/arcsinh

Area Hyperbolic Sine

$\operatorname {arcsinh}$

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 questionable symbol used to denote the area hyperbolic sine function is $\operatorname {arcsinh}$.

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

Also denoted as

arc sinh

$\operatorname {arc sinh}$

A questionable and clumsy symbol used to denote the area hyperbolic sine function is $\operatorname {arc sinh}$.

Its $\LaTeX$ code is \operatorname {arc sinh} .

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inverse hyperbolic function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): arccosh, arcsinh, arctanh, etc.${}$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inverse hyperbolic function