add numerical recipes library

lib/nr/cpp/recipes/bessy0.cpp

@@ -0,0 +1,28 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+DP NR::bessy0(const DP x)
+{
+	DP z,xx,y,ans,ans1,ans2;
+
+	if (x < 8.0) {
+		y=x*x;
+		ans1 = -2957821389.0+y*(7062834065.0+y*(-512359803.6
+			+y*(10879881.29+y*(-86327.92757+y*228.4622733))));
+		ans2=40076544269.0+y*(745249964.8+y*(7189466.438
+			+y*(47447.26470+y*(226.1030244+y*1.0))));
+		ans=(ans1/ans2)+0.636619772*bessj0(x)*log(x);
+	} else {
+		z=8.0/x;
+		y=z*z;
+		xx=x-0.785398164;
+		ans1=1.0+y*(-0.1098628627e-2+y*(0.2734510407e-4
+			+y*(-0.2073370639e-5+y*0.2093887211e-6)));
+		ans2 = -0.1562499995e-1+y*(0.1430488765e-3
+			+y*(-0.6911147651e-5+y*(0.7621095161e-6
+			+y*(-0.934945152e-7))));
+		ans=sqrt(0.636619772/x)*(sin(xx)*ans1+z*cos(xx)*ans2);
+	}
+	return ans;
+}