Difference between revisions of "Derivative of Legendre chi 2"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\dfrac{\mathrm{d}}{\mathrm{d}x} \chi_2(x) = \dfrac{\mathrm{arctanh}(x)}{x},$$ | $$\dfrac{\mathrm{d}}{\mathrm{d}x} \chi_2(x) = \dfrac{\mathrm{arctanh}(x)}{x},$$ | ||
where $\chi$ denotes the [[Legendre chi]] function and $\mathrm{arctanh}$ denotes the [[Arctanh|inverse hyperbolic tangent]] function. | where $\chi$ denotes the [[Legendre chi]] function and $\mathrm{arctanh}$ denotes the [[Arctanh|inverse hyperbolic tangent]] function. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 07:58, 8 June 2016
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.
