26 Numerics library [numerics]
26.9 Mathematical functions for floating-point types [c.math]
26.9.5 Mathematical special functions [sf.cmath]
26.9.5.12 (Incomplete) elliptic integral of the second kind [sf.cmath.ellint_2]
double ellint_2(double k, double phi);
float ellint_2f(float k, float phi);
long double ellint_2l(long double k, long double phi);
Effects: These functions compute the incomplete elliptic integral of the second kind of their respective arguments k and phi (phi measured in radians).
Returns:
![\[%
\mathsf{E}(k, \phi) =
\int_0^\phi \! \sqrt{1 - k^2 \sin^2 \theta} \, \mathsf{d}\theta,
\quad \mbox{for $|k| \le 1$}
\]](math/1756176792287081627.png)
where
k is k and
phi is phi.