# Definition:Spence's Function

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## Contents

## 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.

## Sources

- Weisstein, Eric W. "Dilogarithm." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/Dilogarithm.html