File:TaniaPlot.png

C++ generator of the curve

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
using namespace std;
#include <complex>
typedef complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)

z_type ArcTania(z_type z) {return z + log(z) - 1. ;}

z_type ArcTaniap(z_type z) {return 1. + 1./z ;}

z_type TaniaTay(z_type z) { int n; z_type s;
s=1.+z*(.5+z*(1./16.+z*(-1./192.+z*(-1./3072.+z*(1.3/6144.+z*(-4.7/147456.
//+z*(7.3/4128768.) //some reserve term
)))))); DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }

z_type TaniaNega(z_type z){int n;z_type s=exp(z-exp(z)+1.);
DO(n,4) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }

z_type TaniaBig(z_type z){int n;z_type s=z; s=z-log(s)+1.;
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }

z_type TaniaS(z_type z){int n; z_type s,t=z+z_type(2.,-M_PI);t*=2./9.; t=I*sqrt(t);
s=-1.+t*(3.+t*(-3.+t*(.75+t*(.3+t*(.9/16.+t*(-.3/7.+t*(-12.51/224. //+t*(-.9/28.)
)))))));
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }

z_type Tania(z_type z){ z_type t;
if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);
if( abs(z)>7.

{{Image|TaniaPlot.png|right|350px|Add image caption here.}}