Definition:Spence's Function

Definition
Spence's function, also known as the dilogarithm, is a special case of the polylogarithm, defined for $z \in \C$ by the integral:


 * $\displaystyle \operatorname {Li}_2 \left({z}\right) = -\int_0^z \frac {\mathrm{Ln} \left({1 - t}\right)} t \, \mathrm d t$

where:
 * $\displaystyle \int_0^z$ is an integral across the straight line in the complex plane connecting $0$ and $z$.
 * $\mathrm{Ln}$ is the principal branch of the complex natural logarithm.