Difference between revisions of "Derivative of Legendre chi 2"

Revision as of 17:48, 25 June 2017

Theorem

The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \chi_2(x) = \dfrac{\mathrm{arctanh}(x)}{x},$$ where $\chi$ denotes the Legendre chi function and $\mathrm{arctanh}$ denotes the inverse hyperbolic tangent function.

Proof

References