Difference between revisions of "Polylogarithm"

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The polylogarithm $\mathrm{Li}_s$ is defined by the formula for $|z|<1$ by
 
The polylogarithm $\mathrm{Li}_s$ is defined by the formula for $|z|<1$ by
$$\mathrm{Li}_s(z) = \sum_{k=1}^{\infty} \dfrac{z^k}{k^z} = z + \dfrac{z^2}{2^z} + \dfrac{z^3}{3^z} + \ldots$$
+
$$\mathrm{Li}_s(z) = \sum_{k=1}^{\infty} \dfrac{z^k}{k^s} = z + \dfrac{z^2}{2^s} + \dfrac{z^3}{3^s} + \ldots$$
 
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]].
  

Revision as of 17:06, 19 April 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