Difference between revisions of "Derivative of Legendre chi 2"
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<strong>[[Derivative of Legendre chi|Proposition]]:</strong> The following formula holds: | <strong>[[Derivative of Legendre chi|Proposition]]:</strong> The following formula holds: | ||
| − | $$\dfrac{d}{ | + | $$\dfrac{\mathrm{d}}{\mathrm{d}x} \chi_2(x) = \dfrac{\mathrm{arctanh}(x)}{x},$$ |
where $\chi$ denotes the [[Legendre chi]] function and $\mathrm{arctanh}$ denotes the [[Arctanh|inverse hyperbolic tangent]] function. | where $\chi$ denotes the [[Legendre chi]] function and $\mathrm{arctanh}$ denotes the [[Arctanh|inverse hyperbolic tangent]] function. | ||
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Revision as of 19:08, 15 May 2016
Proposition: The following formula holds: $$\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: █
