File:AuZexLamPlotT.jpg

Explicit plot of functions AuZex (thick black curve) and LambertW (thin red curve).

See AuZex approximation for details.

C++ generator of curves

// Files Tania.cin, LambertW.cin, AuZex.cin, ado.cin should be loaded to the working directory in order to compile the code below.

#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.)

#include "Tania.cin" // need for LambertW
#include "LambertW.cin" // need for AuZex
// #include "SuZex.cin"
#include "AuZex.cin"
#include "ado.cin"
#define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);

main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;  FILE *o;o=fopen("AuZexLam.eps","w");  ado(o,1204,404);
fprintf(o,"2 202 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
for(n=-4;n<3;n++) {M(0,n)L(12,n)}
for(m=0;m<13;m++) {M(m,-2)L(m,2)}
M(M_E,0)L(M_E,1)  fprintf(o,".01 W S\n");
//   DO(m,1300){y=-2. +.01*m; x=Re(suzex(y)); if(m==0) M(x,y) else L(x,y) if(x>12) break;}  fprintf(o,".06 W 0 1 1 RGB S\n");
       DO(m,700){x=.38 +.02*m; y=Re(auzex(x)); if(m==0) M(x,y) else L(x,y) if(x>12.03) break;}  fprintf(o,".023 W 0 0 0 RGB S\n");
       DO(m,700){x=-.03 +.02*m; y=Re(LambertW(x)); if(m==0) M(x,y) else L(x,y) if(x>12.03) break;}  fprintf(o,".011 W 1 0 0 RGB S\n");
fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%');  fclose(o);
      system("epstopdf AuZexLam.eps"); 
      system(    "open AuZexLam.pdf"); //for macintosh
      getchar(); system("killall Preview"); // For macintosh
}

Latex generator of labels

% % Copyleft 2012 by Dmitrii Kouznetsov%<br> \documentclass[12pt]{article} %<br> \usepackage{geometry} %<br> \usepackage{graphicx} %<br> \usepackage{rotating} %<br> \paperwidth 1208pt %<br> \paperheight 405pt %<br> \topmargin -108pt %<br> \oddsidemargin -73pt %<br> \textwidth 1300pt %<br> \textheight 900pt %<br> \pagestyle {empty} %<br> \newcommand \sx {\scalebox} %<br> \newcommand \rot {\begin{rotate}} %<br> \newcommand \ero {\end{rotate}} %<br> \newcommand \ing {\includegraphics} %<br> \parindent 0pt \begin{document}%<br> {\begin{picture}(1204,404) %<br> %\put(1,9){\ing{arclambertw}} %<br> %\put(1,9){\ing{LambertWplot}} %<br> \put(0,0){\ing{AuZexLam}} %<br> \put(13,387){\sx{2.9}{$y$}} %<br> %\put(209,378){\sx{3.1}{$\mathrm e$}} %<br> \put(13,292){\sx{2.8}{$1$}} %<br> \put(13,192){\sx{2.8}{$0$}} %<br> \put(-1,092){\sx{2.8}{$-\!1$}} %<br> \put(267,184){\sx{2.9}{$\mathrm e$}} %<br> \put( 95, 176){\sx{2.8}{$1$}} %<br> \put(195,176){\sx{2.8}{$2$}} %<br> \put(295,176){\sx{2.8}{$3$}} %<br> \put(396,176){\sx{2.8}{$4$}} %<br> \put(496,176){\sx{2.8}{$5$}} %<br> \put(597,176){\sx{2.8}{$6$}} %<br> \put(698,176){\sx{2.8}{$7$}} %<br> \put(798,176){\sx{2.8}{$8$}} %<br> \put(898,176){\sx{2.8}{$9$}} %<br> \put(990,176){\sx{2.8}{$10$}} %<br> \put(1090,176){\sx{2.8}{$11$}} %<br> % \put(300,-9){\sx{2.5}{$0$}} %<br> \put(1189,180){\sx{2.9}{$x$}} %<br> \put(25,240){\sx{2.7}{\rot{17}$y\!=\!\mathrm{LambertW}(x)$\ero}} %<br> \put(914,334){\sx{3.4}{$y\!=\!\mathrm{AuZex}(x)$}} %<br> \end{picture} %<br> } %<br> \end{document}