Symbols:Greek/Pi/Complete Elliptic Integral of the Third Kind

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Complete Elliptic Integral of the Third Kind

$\map \Pi {k, n}$


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

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

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


The $\LaTeX$ code for \(\map \Pi {k, n}\) is \map \Pi {k, n} .