Difference between revisions of "Relationship between Li 2(1),Li 2(-1), and pi"
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==References== | ==References== | ||
| − | {{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x)|next=}}: (1.8) | + | {{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x)|next=Li_2(1)=pi^2/6}}: (1.8) |
Revision as of 00:01, 4 June 2016
Theorem
The following formula holds: $$2\mathrm{Li}_2(1) = 2\mathrm{Li}_2(-1) + \dfrac{\pi^2}{2},$$ where $\mathrm{Li}_2$ denotes the dilogarithm and $\pi$ denotes pi.
Proof
References
1926: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous) ... (next): (1.8)
