Difference between revisions of "Polylogarithm"
From specialfunctionswiki
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The polylogarithm $\mathrm{Li}_s$ is defined by the formula | The polylogarithm $\mathrm{Li}_s$ is defined by the formula | ||
$$\mathrm{Li}_s(z) = \sum_{k=1}^{\infty} \dfrac{z^k}{k^s} = z + \dfrac{z^2}{2^s} + \dfrac{z^3}{3^s} + \ldots$$ | $$\mathrm{Li}_s(z) = \sum_{k=1}^{\infty} \dfrac{z^k}{k^s} = z + \dfrac{z^2}{2^s} + \dfrac{z^3}{3^s} + \ldots$$ | ||
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=Properties= | =Properties= | ||
| − | + | [[Lerch transcendent polylogarithm]]<br /> | |
| − | + | [[Legendre chi in terms of polylogarithm]]<br /> | |
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 16:33, 20 June 2016
The polylogarithm $\mathrm{Li}_s$ is defined by the formula $$\mathrm{Li}_s(z) = \sum_{k=1}^{\infty} \dfrac{z^k}{k^s} = z + \dfrac{z^2}{2^s} + \dfrac{z^3}{3^s} + \ldots$$ A special case of the polylogarithm with $s=2$ is called a dilogarithm.
Various polylogarithms plotted on $[-2,1]$.
Videos
Properties
Lerch transcendent polylogarithm
Legendre chi in terms of polylogarithm
