26 Numerics library [numerics]

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

26.8.6 Mathematical special functions [sf.cmath]

26.8.6.12 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.