Difference between revisions of "Li 2(1)=pi^2/6"
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(Created page with "==Theorem== The following formula holds: $$\mathrm{Li}_2(1) = \dfrac{\pi^2}{6},$$ where $\mathrm{Li}$ denotes the dilogarithm and $\pi$ denotes pi. ==References== {{B...") |
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$$\mathrm{Li}_2(1) = \dfrac{\pi^2}{6},$$ | $$\mathrm{Li}_2(1) = \dfrac{\pi^2}{6},$$ | ||
where $\mathrm{Li}$ denotes the [[dilogarithm]] and $\pi$ denotes [[pi]]. | where $\mathrm{Li}$ denotes the [[dilogarithm]] and $\pi$ denotes [[pi]]. | ||
| + | |||
| + | ==Proof== | ||
==References== | ==References== | ||
{{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Relationship between Li 2(1),Li 2(-1), and pi|next=}}: (1.9) | {{BookReference|Polylogarithms and Associated Functions|1926|ed=2nd|edpage=Second Edition|Leonard Lewin|prev=Relationship between Li 2(1),Li 2(-1), and pi|next=}}: (1.9) | ||
Revision as of 00:03, 4 June 2016
Theorem
The following formula holds: $$\mathrm{Li}_2(1) = \dfrac{\pi^2}{6},$$ where $\mathrm{Li}$ denotes the dilogarithm and $\pi$ denotes pi.
Proof
References
1926: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (previous): (1.9)
