Difference between revisions of "Lerch transcendent polylogarithm"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Proposition:</strong> The following formula holds: $$\Phi(z,n,1)=\dfrac{\math...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\Phi(z,n,1)=\dfrac{\mathrm{Li}_n(z)}{z},$$ | $$\Phi(z,n,1)=\dfrac{\mathrm{Li}_n(z)}{z},$$ | ||
where $\Phi$ denotes the [[Lerch transcendent]] and $\mathrm{Li_n}$ denotes the [[polylogarithm]]. | where $\Phi$ denotes the [[Lerch transcendent]] and $\mathrm{Li_n}$ denotes the [[polylogarithm]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 16:33, 20 June 2016
Theorem
The following formula holds: $$\Phi(z,n,1)=\dfrac{\mathrm{Li}_n(z)}{z},$$ where $\Phi$ denotes the Lerch transcendent and $\mathrm{Li_n}$ denotes the polylogarithm.
