28 Numerics library [numerics]

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

28.7.6 Mathematical special functions [sf.cmath]

28.7.6.12 Incomplete elliptic integral of the first kind [sf.cmath.ellint.1]

floating-point-type ellint_1(floating-point-type k, floating-point-type 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), where F is given by Formula 28.32, k is k, and φ is phi.

\begin{matrix} F (k, ϕ) = \int_{0}^{ϕ} \frac{d θ}{\sqrt{1 - k^{2} {sin}^{2} θ}}, for | k | \leq 1 \\ (28.32) \end{matrix}