Spence's function
Sign in to savethumb|right|325px|The dilogarithm along the real axis thumb|right|325px|The principal value of the dilogarithm plotted in the complex plane
Article
10 sectionsContents
- Analytic structure
- Identities
- Particular value identities
- Special values
- In particle physics
- See also
- Notes
- References
- Further reading
- External links
thumb|right|325px|The dilogarithm along the real axis thumb|right|325px|The principal value of the dilogarithm plotted in the complex plane
In mathematics, the dilogarithm (or '''Spence's function'''), denoted as , is a particular case of the polylogarithm. Two related special functions are referred to as Spence's function, the dilogarithm itself: \operatorname{Li}_2(z) = -\int_0^z{\ln(1-u) \over u}\, du \text{, }z \in \Complex and its reflection. For , an infinite series also applies (the integral definition constitutes its analytical extension to the complex plane): \operatorname{Li}_2(z) = \sum_{k=1}^\infty {z^k \over k^2}.