Difference between revisions of "Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3"
From specialfunctionswiki
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==References== | ==References== | ||
| − | * {{BookReference|Higher Transcendental Functions Volume I|1953| | + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Li2(z)=zPhi(z,2,1)|next=findme}}: $\S 1.11.1 (23)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 23:23, 3 March 2018
Theorem
The following formula holds: $$\mathrm{Li}_2(z)=-\mathrm{Li}_2 \left( \dfrac{1}{z} \right) - \dfrac{\log(z)^2}{2} + i \pi \log(z) + \dfrac{\pi^2}{3},$$ where $\mathrm{Li}_2$ denotes the dilogarithm, $\log$ denotes the logarithm, $i$ denotes the imaginary number, and $\pi$ denotes pi.
Proof
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.11.1 (23)$
