Definition:Spence's Function

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

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


$\ds \int_0^z$ 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.

Also see

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

Source of Name

This entry was named for William Spence.