Difference between revisions of "Derivative of Legendre chi 2"
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$\dfrac{\mathrm{d}}{\mathrm{d}x} \chi_2( | + | $$\dfrac{\mathrm{d}}{\mathrm{d}x} \chi_2(z) = \dfrac{\mathrm{arctanh}(z)}{z},$$ |
where $\chi$ denotes the [[Legendre chi]] function and $\mathrm{arctanh}$ denotes the [[Arctanh|inverse hyperbolic tangent]] function. | where $\chi$ denotes the [[Legendre chi]] function and $\mathrm{arctanh}$ denotes the [[Arctanh|inverse hyperbolic tangent]] function. | ||
Revision as of 17:48, 25 June 2017
Theorem
The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \chi_2(z) = \dfrac{\mathrm{arctanh}(z)}{z},$$ where $\chi$ denotes the Legendre chi function and $\mathrm{arctanh}$ denotes the inverse hyperbolic tangent function.
