File:Autraplot.jpg

Explicit plot of function AuTra and two its asymptotics.

This image is used as figure 20.9 of the Book Superfunction (In Russian, 2014; the English version is in preparation, 2015) .

Function SuTra as entire function with logarithmic asymptotic is described also in year 2013 at Hikari .

C++ generator of curves
Files ado.cin, conto.cin, sutran.cin should be loaded to the working directory in order to compile the code below // using namespace std; typedef std::complex z_type; z_type tra(z_type z){ return exp(z)+z;}
 * 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 "arctran.cin"
 * 3) include "sutran.cin"
 * 4) include "autran.cin"

int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("autraplo.eps","w");  ado(o,412,412); fprintf(o,"104 204 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); for(n=-2;n<3;n++) {M(-1,n)L(3,n)} for(m=-1;m<4;m++) {M(m,-2)L(m,2)} // M(M_E,0)L(M_E,1) M(0,M_E)L(1,M_E) //M(0,1.+M_E) L(2,1.+M_E) fprintf(o,".004 W S\n"); //DO(m,700){x=-2.01 +.02*m; y=Re(sutran(x)); if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 1 RGB S\n"); //DO(m,740){x=-3.1 +.02*m; y=Re(sutran(x)); if(m==0) M(y,x) else L(y,x) if(x>3.03||y>6.01) break;} fprintf(o,".03 W 0 1 1 RGB S\n"); //DO(m,740){x=-1.25 +.02*m; y=Re(autra(x)); if(m==0) M(x,y) else L(x,y) if(x>6.03||y>6.01) break;} fprintf(o,".03 W 1 .5 0 RGB S\n"); DO(m,740){x=-1.1 +.02*m; y=Re(autran(x)); if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".03 W 1 0 0 RGB S\n"); DO(m,740){x=-1.1 +.02*m; y=.5*x-exp(-x)+1.1259817765745026; if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 0 RGB S\n"); DO(m,740){x=-1.1 +.02*m; y=.5*x-exp(-x)+1.1259817765745026-exp(x)/6.; if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 0 RGB S\n"); //DO(m,740){x=-1.25 +.02*m; y=.5*x-exp(-x)+1.1259817765745026-exp(x)/6.+exp(2*x)/16; if(m==0) M(x,y) else L(x,y) if(x>6.03||y>6.01) break;} fprintf(o,".01 W 0 0 0 RGB S\n"); fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); system("epstopdf autraplo.eps"); system(   "open autraplo.pdf"); //for macintosh getchar; system("killall Preview"); // For macintosh }
 * 1) define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
 * 2) define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);

Latex generator of labels
\documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphicx} \usepackage{rotating} \paperwidth 406pt \paperheight 412pt \topmargin -98pt \oddsidemargin -75.6pt \textwidth 900pt \textheight 900pt \pagestyle {empty} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \parindent 0pt \pagestyle{empty} \begin{document} \begin{picture}(402,404) \put(112,391){\sx{2.2}{$y$}} \put(112,296){\sx{2.2}{$1$}} \put(112,196){\sx{2.2}{$0$}} \put(102, 96){\sx{2.2}{$-1$}} \put(99,180){\sx{2.2}{$0$}} \put(199,180){\sx{2.2}{$1$}} \put(299,180){\sx{2.2}{$2$}} \put(390,180){\sx{2.2}{$x$}} \put(0,0){\ing{autraplo}} \put(153,303){\sx{2}{\rot{35}$y\!=\!x_0\!+\!x/2\!-\!\mathrm e^{-x}$\ero}} \put(267,325){\sx{2.2}{\rot{17}$y\!=\!\mathrm{AuTra}(x)$\ero}} %\put(185,128){\sx{2.2}{$y\!=\!x/2\!-\!\mathrm e^x\!+\!1.1259817765745026-exp(x)/6.+exp(2*x)/16)$}} \put(166,122){\sx{2}{$y\!=\!x_0\!+\!x/2\!-\!\mathrm e^{-x}\!+\!\mathrm e^x/6$}} \end{picture} \end{document}