Difference between revisions of "Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x)"
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{{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Derivative of Li 2(-1/x)|next=Relationship between Li_2(1),Li_2(-1), and pi}}: (1.7) | {{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Derivative of Li 2(-1/x)|next=Relationship between Li_2(1),Li_2(-1), and pi}}: (1.7) | ||
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| + | [[Category:Unproven]] | ||
Revision as of 07:18, 16 June 2016
Theorem
The following formula holds: $$\mathrm{Li}_2 \left( - \dfrac{1}{x} \right) + \mathrm{Li}_2(-x) = 2\mathrm{Li}_2(-1) - \dfrac{\log^2(x)}{2},$$ 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): (1.7)
