#include <cmath>

 double cyl_bessel_j(double nu, double x)  // C++17

Liefert Wert der Bessel-Funktion 1. Art $J_\nu(x) = \sum_{k=0}^\infty \frac{(-1)^k(x/2)^{\nu+2k}}{k! \Gamma(\nu+k+1)} = \frac{1}{\pi}\int_0^\pi \cos(x \sin \theta -\nu\theta) d\theta - \frac{\sin(\nu \pi)}{\pi} \int_0^\infty e^{-x \sinh t - \nu t} dt$ für $x \geq 0$.

Rückgabewert: $J_\nu(x)$.

cyl_bessel_i(), cyl_bessel_k(), cyl_neumann().

cyl_bessel_j.cpp

#include <cmath>
#include <iostream>
 
int main()
{
  std::cout << "# x n=0 n=1 n=2\n";
 
  for (int i = 0; i <= 1000; ++i)
  {
    double x = 0.01*i;
    std::cout << x 
      << '\t' << std::cyl_bessel_j(0, x) 
      << '\t' << std::cyl_bessel_j(1, x) 
      << '\t' << std::cyl_bessel_j(2, x) 
      << '\n';
  }
}