Difference between revisions of "Derivative of Li 2(-1/x)"
From specialfunctionswiki
(Created page with "==Theorem== The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \mathrm{Li}_2 \left( -\dfrac{1}{x} \right) = \dfrac{\log(1+\frac{1}{x})}{x} = \dfrac{\log(1+x)-\log(...") |
(No difference)
|
Revision as of 23:54, 3 June 2016
Theorem
The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \mathrm{Li}_2 \left( -\dfrac{1}{x} \right) = \dfrac{\log(1+\frac{1}{x})}{x} = \dfrac{\log(1+x)-\log(x)}{x},$$ where $\mathrm{Li}_2$ denotes the dilogarithm and $\log$ denotes the logarithm.
Proof
References
1926: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous): (1.6)
