add numerical recipes library

lib/nr/cpp/recipes/plgndr.cpp

@@ -0,0 +1,36 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+DP NR::plgndr(const int l, const int m, const DP x)
+{
+	int i,ll;
+	DP fact,pll,pmm,pmmp1,somx2;
+
+	if (m < 0 || m > l || fabs(x) > 1.0)
+		nrerror("Bad arguments in routine plgndr");
+	pmm=1.0;
+	if (m > 0) {
+		somx2=sqrt((1.0-x)*(1.0+x));
+		fact=1.0;
+		for (i=1;i<=m;i++) {
+			pmm *= -fact*somx2;
+			fact += 2.0;
+		}
+	}
+	if (l == m)
+		return pmm;
+	else {
+		pmmp1=x*(2*m+1)*pmm;
+		if (l == (m+1))
+			return pmmp1;
+		else {
+			for (ll=m+2;ll<=l;ll++) {
+				pll=(x*(2*ll-1)*pmmp1-(ll+m-1)*pmm)/(ll-m);
+				pmm=pmmp1;
+				pmmp1=pll;
+			}
+			return pll;
+		}
+	}
+}