Definition:Complete Elliptic Integral of the Third Kind/Definition 2

From ProofWiki
Jump to navigation Jump to search

Special Function

$\ds \map \Pi {k, n} = \int \limits_0^1 \frac {\d v} {\paren {1 + n v^2} \sqrt {\paren {1 - v^2} \paren {1 - k^2 v^2} } }$

is the complete elliptic integral of the third kind, and is a function of the variables:

$k$, defined on the interval $0 < k < 1$
$n \in \Z$


Also see


Sources