Symbols:F/Incomplete Elliptic Integral of the First Kind

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Incomplete Elliptic Integral of the First Kind

$\map F {k, \phi}$


$\ds \map F {k, \phi} = \int \limits_0^\phi \frac {\d \phi} {\sqrt {1 - k^2 \sin^2 \phi} }$

is the incomplete elliptic integral of the first kind, and is a function of the variables:

$k$, defined on the interval $0 < k < 1$
$\phi$, defined on the interval $0 \le \phi \le \pi / 2$.


The $\LaTeX$ code for \(\map F {k, \phi}\) is \map F {k, \phi} .