Difference between revisions of "Polylogarithm"

From specialfunctionswiki
Jump to: navigation, search
 
(9 intermediate revisions by the same user not shown)
Line 1: Line 1:
The polylogarithm $\mathrm{Li}_s$ is defined by the formula
+
__NOTOC__
 +
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]].
  
 
<div align="center">
 
<div align="center">
Line 9: Line 11:
  
 
=Properties=
 
=Properties=
{{:Lerch transcendent polylogarithm}}
+
[[Lerch transcendent polylogarithm]]<br />
 +
[[Legendre chi in terms of polylogarithm]]<br />
 +
 
 +
=Videos=
 +
[https://www.youtube.com/watch?v=6v60ivoC2z8 polylogarithm function]
 +
 
 +
=References=
 +
 
 +
{{:Logarithm and friends footer}}
 +
 
 +
[[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