Symbols:A/Area Hyperbolic Tangent/arctanh

Area Hyperbolic Tangent

$\operatorname {arctanh}$

The inverse hyperbolic tangent $\artanh: S \to \R$ is a real function defined on $S$ as:

$\forall x \in S: \map \artanh x := \dfrac 1 2 \map \ln {\dfrac {1 + x} {1 - x} }$

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

A questionable symbol used to denote the area hyperbolic tangent function is $\operatorname {arctanh}$.

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

Also denoted as

arc tanh

$\operatorname {arc tanh}$

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

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

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.${}$