26 Numerics library [numerics]
26.9 Mathematical functions for floating-point types [c.math]
26.9.5 Mathematical special functions [sf.cmath]
26.9.5.11 (Incomplete) elliptic integral of the first kind [sf.cmath.ellint_1]
double ellint_1(double k, double phi);
float ellint_1f(float k, float phi);
long double ellint_1l(long double k, long double phi);
Effects: These functions compute the incomplete elliptic integral of the first kind of their respective arguments k and phi (phi measured in radians).
Returns:
![\[%
\mathsf{F}(k, \phi) =
\int_0^\phi \! \frac{\mathsf{d}\theta}
{\sqrt{1 - k^2 \sin^2 \theta}},
\quad \mbox{for $|k| \le 1$}
\]](math/4296002783603320886.png)
where
k is k and
phi is phi.