File:Doya1T.jpg

Explicit plot of Doya function and two its polynomial approximations at zero;

$y=\mathrm{Doya}(x)$

$y=\mathrm e x$

$y=\mathrm e x - \mathrm e(\mathrm e \!-\!1) x^2$

C++ generator of curces
Files ado.cin and doya.cin should be loaded into the working directory in order to compile the code below.

// using namespace std; typedef std::complex z_type; DB ArcTania(DB x){ return x+log(x)-1.;} int main{ int j,k,m,n; DB x,y,t,e, a; z_type z; FILE *o;o=fopen("doyaplot1.eps","w");ado(o,208,308); fprintf(o,"4 4 translate\n 100 100 scale\n"); fprintf(o,"2 setlinecap\n"); for(m=0;m<3;m++){ M(m,0)L(m,3)} for(n=0;n<4;n++){ M(0,n)L(2,n)} fprintf(o,".004 W 0 0 0 RGB S\n"); fprintf(o,"2 setlinejoin 1 setlinecap\n"); M(0,0); for(n=1;n<151;n++){x=.02*n;z=x;y=Re(Doya(1.,z)); L(x,y)} fprintf(o,".02 W 0 .8 0 RGB S\n");
 * 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.)
 * 1) include "ado.cin"
 * 2) include "doya.cin"
 * 3) define M(x,y) fprintf(o,"%7.4f %7.4f M\n",0.+x,0.+y);
 * 4) define L(x,y) fprintf(o,"%7.4f %7.4f L\n",0.+x,0.+y);

M(0,0); for(n=1;n<58;n++){x=.01*n; y=M_E*x*(1.-x*(M_E-1.)) ; L(x,y)} fprintf(o,".005 W .8 0 0 RGB S\n");

M(0,0) L(3./M_E,3.) fprintf(o,".005 W 0 0 .8 RGB S\n");

//M(0,0); for(n=0;n<110;n++){x=.01+.01*n; y=M_E*x*(1.+x*(1.-M_E + x*(.5+M_E*(-2.+M_E*1.5)))) ; L(x,y)}

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o); system("epstopdf doyaplot1.eps"); system(   "open doyaplot1.pdf"); //these 2 commands may be specific for macintosh getchar; system("killall Preview");// if run at another operational sysetm, may need to modify }

Latex generator of labels
\documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphicx} \usepackage{rotating} \paperwidth 214pt \paperheight 320pt \topmargin -100pt \oddsidemargin -83pt \textwidth 1200pt \textheight 600pt \pagestyle {empty} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \begin{document} \begin{picture}(200,298) \put(0,0){\ing{doyaplot1}} \put(-7,298){\sx{1.6}{$y$}} %\put(-36,300){\sx{1.7}{$T(z)$}} \put(-7,200){\sx{1.6}{$2$}} \put(-7,100){\sx{1.6}{$1$}} \put(0,-11){\sx{1.6}{0}} \put(100,-11){\sx{1.6}{1}} \put(197,-11){\sx{1.6}{$x$}} \put( 38,110){\rot{70}{\sx{1.7}{$y=\mathrm e\, x$}}\ero} %\put( 58,110){\rot{55}{\sx{1.7}{$y=T(z)$}}\ero} \put( 58,110){\rot{53}{\sx{1.7}{$y=\mathrm{Doya}(x)$}}\ero} \put( 26,30){\sx{1.6}{$y=\mathrm e\, z - \mathrm e (\mathrm e\!-\!1) x^2$}} \end{picture} \end{document}