Derivative of Legendre chi 2
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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.
