Arctanh

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The inverse hyperbolic tangent function $\mathrm{arctanh}$ is the inverse function of the hyperbolic tangent function. It may be defined by $$\mathrm{arctanh}(z) = \dfrac{\log(1+z)}{2} - \dfrac{\log(1-z)}{2},$$ where $\log$ denotes the logarithm.

Properties[edit]

Derivative of arctanh
Antiderivative of arctanh
Derivative of Legendre chi

See also[edit]

Arctan
Tanh
Tangent

Inverse hyperbolic trigonometric functions