Difference between revisions of "Arctanh"
From specialfunctionswiki
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File:Arctanhplot.png|Plot of $\mathrm{arctanh}$ on $(-1,1)$. | File:Arctanhplot.png|Plot of $\mathrm{arctanh}$ on $(-1,1)$. | ||
| − | File: | + | File:Complexarctanhplot.png|[[Domain coloring]] of $\mathrm{arctanh}$. |
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Revision as of 01:44, 16 September 2016
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.
Plot of $\mathrm{arctanh}$ on $(-1,1)$.
Domain coloring of $\mathrm{arctanh}$.
Properties
Derivative of arctanh
Derivative of Legendre chi
