Definition:Elliptic Integral of the First Kind/Complete/Definition 1

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Special Function

$\displaystyle \map K k = \int \limits_0^{\pi / 2} \frac {\d \phi} {\sqrt {1 - k^2 \sin^2 \phi} }$

is the complete elliptic integral of the first kind, and is a function of $k$, defined on the interval $0 < k < 1$.


Also see


Sources