Definition:Spence's Function

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


 * $\ds \map {\Li_2} z = -\int_0^z \frac {\map \Ln {1 - t} } t \rd t$

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

Also known as
Spence's function is also known as the dilogarithm function.