Difference between revisions of "Arctanh"
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| + | File:Arctanhplot.png|Plot of $\mathrm{arctanh}$ on $(-1,1)$. | ||
File:Complex ArcTanh.jpg|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{arctanh}$. | File:Complex ArcTanh.jpg|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{arctanh}$. | ||
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Revision as of 09:33, 9 November 2015
Plot of $\mathrm{arctanh}$ on $(-1,1)$.
Domain coloring of analytic continuation of $\mathrm{arctanh}$.
Contents
Properties
Theorem
The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \chi_2(z) = \dfrac{\mathrm{arctanh}(z)}{z},$$ where $\chi$ denotes the Legendre chi function and $\mathrm{arctanh}$ denotes the inverse hyperbolic tangent function.
