code: public static double Y0(double x) {
          if (x < 8.0) {
              double y = x * x;
  
              double ans1 = -2957821389.0 + y * (7062834065.0 + y * (-512359803.6
                      + y * (10879881.29 + y * (-86327.92757 + y * 228.4622733))));
              double ans2 = 40076544269.0 + y * (745249964.8 + y * (7189466.438
                      + y * (47447.26470 + y * (226.1030244 + y * 1.0))));
  
              return (ans1 / ans2) + 0.636619772 * J0(x) * Math.log(x);
          } else {
              double z = 8.0 / x;
              double y = z * z;
              double xx = x - 0.785398164;
  
              double ans1 = 1.0 + y * (-0.1098628627e-2 + y * (0.2734510407e-4
                      + y * (-0.2073370639e-5 + y * 0.2093887211e-6)));
              double ans2 = -0.1562499995e-1 + y * (0.1430488765e-3
                      + y * (-0.6911147651e-5 + y * (0.7621095161e-6
                      + y * (-0.934945152e-7))));
              return Math.sqrt(0.636619772 / x) *
                      (Math.sin(xx) * ans1 + z * Math.cos(xx) * ans2);
          }
      }
docs: Bessel function of the second kind, of order 0.
  
  @param x Value.
  @return Y0 value.