# 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:

$\displaystyle \operatorname {Li}_2 \paren z = -\int_0^z \frac {\Ln \paren {1 - t} } t \rd t$

where:

$\displaystyle \int_0^z$ 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 see

• Results about Spence's Function can be found here.

## Source of Name

This entry was named for William Spence.