#include <cmath>

  double ellint_1(double k, double phi)  // C++17

Liefert Wert des unvollständigen Elliptischen Integrals 1. Art $F(k,\varphi) = \int_0^\varphi \frac{d\theta}{\sqrt{1-k^2 \sin^2 \theta}}$.

Rückgabewert: $F(k,\varphi)$.

ellint_2(), ellint_3(), comp_ellint_1(), comp_ellint_2(), comp_ellint_3().

ellint_1.cpp

#include <cmath>
#include <iostream>
 
int main()
{
  const auto pi = std::acos(-1.0);
 
  std::cout << "# k=0 k=0.7 k=1\n";
 
  for (int i = 0; i < 100; ++i)
  {
    double phi = 0.01*i*pi/2;
    std::cout << phi 
      << '\t' << std::ellint_1(0.0, phi)
      << '\t' << std::ellint_1(0.7, phi)
      << '\t' << std::ellint_1(1.0, phi)
      << '\n';
  }
}