24 Numerics library [numerics]

24.9 Mathematical functions for floating-point types [c.math]

24.9.5 Mathematical special functions [sf.cmath]

24.9.5.11 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:

$F (k, ϕ) = \int_{0}^{ϕ} \frac{d θ}{\sqrt{1 - k^{2} sin^{2} θ}}, for | k | \leq 1,$

where k is k and φ is phi.