29 Numerics library [numerics]

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

29.9.5 Mathematical special functions [sf.cmath] 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).


Π(ν,k,ϕ)=ϕ0dθ(1νsin2θ)1k2sin2θ,for |k|1

where ν is nu, k is k, and φ is phi.