Difference between revisions of "Dilogarithm"

From specialfunctionswiki
Jump to: navigation, search
(Properties)
Line 26: Line 26:
 
[http://maths.dur.ac.uk/~dma0hg/dilog.pdf The Dilogarithm function]<br />
 
[http://maths.dur.ac.uk/~dma0hg/dilog.pdf The Dilogarithm function]<br />
 
[http://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/978-3-540-30308-4_1/fulltext.pdf]<br />
 
[http://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/978-3-540-30308-4_1/fulltext.pdf]<br />
 +
 +
{{:Logarithm and friends footer}}
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 20:27, 25 June 2017

The dilogarithm function $\mathrm{Li}_2$ is defined for $|z| \leq 1$ by $$\mathrm{Li}_2(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{k^2},$$ which is a special case of the polylogarithm.

Properties

Relationship between dilogarithm and log(1-z)/z
Relationship between Li 2(1),Li 2(-1), and pi
Li 2(1)=pi^2/6
Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x)
Derivative of Li 2(-1/x)
Li2(z)=zPhi(z,2,1)

References

(page 31)
The Dilogarithm function
[1]

Logarithm and friends