add numerical recipes library

lib/nr/k_and_r/recipes/hypser.c

@@ -0,0 +1,34 @@
+
+#include "complex.h"
+#define ONE Complex(1.0,0.0)
+
+void hypser(a,b,c,z,series,deriv)
+fcomplex *deriv,*series,a,b,c,z;
+{
+	void nrerror();
+	int n;
+	fcomplex aa,bb,cc,fac,temp;
+
+	deriv->r=0.0;
+	deriv->i=0.0;
+	fac=Complex(1.0,0.0);
+	temp=fac;
+	aa=a;
+	bb=b;
+	cc=c;
+	for (n=1;n<=1000;n++) {
+		fac=Cmul(fac,Cdiv(Cmul(aa,bb),cc));
+		deriv->r+=fac.r;
+		deriv->i+=fac.i;
+		fac=Cmul(fac,RCmul(1.0/n,z));
+		*series=Cadd(temp,fac);
+		if (series->r == temp.r && series->i == temp.i) return;
+		temp= *series;
+		aa=Cadd(aa,ONE);
+		bb=Cadd(bb,ONE);
+		cc=Cadd(cc,ONE);
+
+	}
+	nrerror("convergence failure in hypser");
+}
+#undef ONE