Difference between revisions of "Derivative of Legendre chi 2"
From specialfunctionswiki
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$\dfrac{\mathrm{d}}{\mathrm{d} | + | $$\dfrac{\mathrm{d}}{\mathrm{d}z} \chi_2(z) = \dfrac{\mathrm{arctanh}(z)}{z},$$ |
where $\chi$ denotes the [[Legendre chi]] function and $\mathrm{arctanh}$ denotes the [[Arctanh|inverse hyperbolic tangent]] function. | where $\chi$ denotes the [[Legendre chi]] function and $\mathrm{arctanh}$ denotes the [[Arctanh|inverse hyperbolic tangent]] function. | ||
Latest revision as of 01:31, 1 July 2017
Theorem
The following formula holds: $$\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.
