Category:Definitions/Spence's Function

This category contains definitions related to Spence's Function.
Related results can be found in Category:Spence's Function.

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.