Difference between revisions of "Li2(z)=zPhi(z,2,1)"
From specialfunctionswiki
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Relationship between dilogarithm and log(1-z)/z|next= | + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Relationship between dilogarithm and log(1-z)/z|next=Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3}}: $\S 1.11.1 (22)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 16:10, 10 July 2017
Theorem
The following formula holds: $$\mathrm{Li}_2(z)=z\Phi(z,2,1),$$ where $\mathrm{Li}_2$ denotes the dilogarithm and $\Phi$ denotes the Lerch transcendent.
Proof
References
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.11.1 (22)$
