Difference between revisions of "Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x)"
From specialfunctionswiki
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | {{BookReference|Polylogarithms and Associated Functions| | + | {{BookReference|Polylogarithms and Associated Functions|1981|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}}: $(1.7)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 04:21, 30 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
1981: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous) ... (next): $(1.7)$
