Difference between revisions of "Arctanh"
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Revision as of 18:46, 24 May 2016
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.
