26 Numerics library [numerics]
26.9 Mathematical functions for floating-point types [c.math]
26.9.5 Mathematical special functions [sf.cmath]
26.9.5.13 (Incomplete) elliptic integral of the third kind [sf.cmath.ellint_3]
double ellint_3(double k, double nu, double phi);
float ellint_3f(float k, float nu, float phi);
long double ellint_3l(long double k, long double nu, long double phi);
Effects: These functions compute the incomplete elliptic integral of the third kind of their respective arguments k, nu, and phi (phi measured in radians).
Returns:
![\[%
\mathsf{\Pi}(\nu, k, \phi) =
\int_0^\phi \! \frac{ \mathsf{d}\theta }
{ (1 - \nu \, \sin^2 \theta) \sqrt{1 - k^2 \sin^2 \theta} },
\quad \mbox{for $|k| \le 1$}
\]](math/4836649422931108564.png)
where
nu is nu,
k is k, and
phi is phi.