Difference between revisions of "Polylogarithm"

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The polylogarithm $\mathrm{Li}_s$ is defined by the formula
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The polylogarithm $\mathrm{Li}_s$ is defined by the formula for $|z|<1$ by
 
$$\mathrm{Li}_s(z) = \sum_{k=1}^{\infty} \dfrac{z^k}{k^s} = z + \dfrac{z^2}{2^s} + \dfrac{z^3}{3^s} + \ldots$$
 
$$\mathrm{Li}_s(z) = \sum_{k=1}^{\infty} \dfrac{z^k}{k^s} = z + \dfrac{z^2}{2^s} + \dfrac{z^3}{3^s} + \ldots$$
 
A special case of the polylogarithm with $s=2$ is called a [[dilogarithm]].
 
A special case of the polylogarithm with $s=2$ is called a [[dilogarithm]].
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=Properties=
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[[Lerch transcendent polylogarithm]]<br />
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[[Legendre chi in terms of polylogarithm]]<br />
  
 
=Videos=
 
=Videos=
 
[https://www.youtube.com/watch?v=6v60ivoC2z8 polylogarithm function]
 
[https://www.youtube.com/watch?v=6v60ivoC2z8 polylogarithm function]
  
=Properties=
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=References=
{{:Lerch transcendent polylogarithm}}
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{{:Legendre chi in terms of polylogarithm}}
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{{:Logarithm and friends footer}}
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 20:28, 25 June 2017

The polylogarithm $\mathrm{Li}_s$ is defined by the formula for $|z|<1$ by $$\mathrm{Li}_s(z) = \sum_{k=1}^{\infty} \dfrac{z^k}{k^s} = z + \dfrac{z^2}{2^s} + \dfrac{z^3}{3^s} + \ldots$$ A special case of the polylogarithm with $s=2$ is called a dilogarithm.

Properties

Lerch transcendent polylogarithm
Legendre chi in terms of polylogarithm

Videos

polylogarithm function

References

Logarithm and friends