26 Numerics library [numerics]

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

26.8.6 Mathematical special functions [sf.cmath]

26.8.6.13 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:

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

where k is k and φ is phi.