Difference between revisions of "Derivative of Li 2(-1/x)"
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==References== | ==References== | ||
{{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Relationship between dilogarithm and log(1-z)/z|next=Relationship between Li_2(-1/x),Li_2(-x),Li_2(-1), and log^2(x)}}: (1.6) | {{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Relationship between dilogarithm and log(1-z)/z|next=Relationship between Li_2(-1/x),Li_2(-x),Li_2(-1), and log^2(x)}}: (1.6) | ||
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 20:24, 27 June 2016
Theorem
The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \mathrm{Li}_2 \left( -\dfrac{1}{x} \right) = \dfrac{\log \left(1+\frac{1}{x} \right)}{x} = \dfrac{\log(1+x)-\log(x)}{x},$$ where $\mathrm{Li}_2$ denotes the dilogarithm and $\log$ denotes the logarithm.
Proof
References
1926: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous) ... (next): (1.6)
