#include <math.h>

float bessk1(x)
float x;
{
	double y,ans;
	float bessi1();

	if (x <= 2.0) {
		y=x*x/4.0;
		ans=(log(x/2.0)*bessi1(x))+(1.0/x)*(1.0+y*(0.15443144
			+y*(-0.67278579+y*(-0.18156897+y*(-0.1919402e-1
			+y*(-0.110404e-2+y*(-0.4686e-4)))))));
	} else {
		y=2.0/x;
		ans=(exp(-x)/sqrt(x))*(1.25331414+y*(0.23498619
			+y*(-0.3655620e-1+y*(0.1504268e-1+y*(-0.780353e-2
			+y*(0.325614e-2+y*(-0.68245e-3)))))));
	}
	return ans;
}