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.

using namespace std; typedef complex z_type;
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)

// #include "SuZex.cin"
 * 1) include "Tania.cin" // need for LambertW
 * 2) include "LambertW.cin" // need for AuZex
 * 1) include "AuZex.cin"
 * 2) include "ado.cin"
 * 3) define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
 * 4) 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% \documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphicx} %<br \usepackage{rotating} \paperwidth 1208pt \paperheight 405pt \topmargin -108pt \oddsidemargin -73pt \textwidth 1300pt \textheight 900pt \pagestyle {empty} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \parindent 0pt \begin{document}% {\begin{picture}(1204,404) \put(0,0){\ing{AuZexLam}} \put(13,387){\sx{2.9}{$y$}} %\put(209,378){\sx{3.1}{$\mathrm e$}} \put(13,292){\sx{2.8}{$1$}} \put(13,192){\sx{2.8}{$0$}} \put(-1,092){\sx{2.8}{$-\!1$}} \put(267,184){\sx{2.9}{$\mathrm e$}} \put( 95, 176){\sx{2.8}{$1$}} \put(195,176){\sx{2.8}{$2$}} \put(295,176){\sx{2.8}{$3$}} \put(396,176){\sx{2.8}{$4$}} \put(496,176){\sx{2.8}{$5$}} \put(597,176){\sx{2.8}{$6$}} \put(698,176){\sx{2.8}{$7$}} \put(798,176){\sx{2.8}{$8$}} \put(898,176){\sx{2.8}{$9$}} \put(990,176){\sx{2.8}{$10$}} \put(1090,176){\sx{2.8}{$11$}} % \put(300,-9){\sx{2.5}{$0$}} \put(1189,180){\sx{2.9}{$x$}} \put(25,240){\sx{2.7}{\rot{17}$y\!=\!\mathrm{LambertW}(x)$\ero}} \put(914,334){\sx{3.4}{$y\!=\!\mathrm{AuZex}(x)$}} \end{picture} } \end{document}