File:ShokopPlotAT.png

Shoko function $y = \mathrm{Shoko}(t) = \ln\!\Big(1+\mathrm e^x (\mathrm e\!-\!1)\Big)$ and two its asymptotics versus $x$.

Generator of curves

// File ado.cin should be stored in the working directory in order to compile the C++ code below:

#include<math.h>
#include<stdio.h>
#include<stdlib.h>
#define DB double
#include "ado.cin"

DB Shoko(DB x) { return log(1.+exp(x)*(M_E-1.)); }

main(){ int m,n; double x,y; FILE *o;
o=fopen("ShokoPlotA.eps","w"); ado(o,802,460);
fprintf(o,"401 1 translate 100 100 scale\n");
#define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);
for(m=-4;m<5;m++) {M(m,0)L(m,4)}
for(m=0;m<5;m++) {M(-4,m)L(4,m)}
fprintf(o,"2 setlinecap .01 W S\n");
for(m=0;m<81;m++) {x=-4.+.1*m; y=Shoko(x); if(m==0) M(x,y) else L(x,y);}
fprintf(o,"1 setlinecap 1 setlinejoin .05 W 0 .5 0 RGB S\n");
for(m=0;m<51;m++) {x=-4.+.1*m; y=(M_E-1)*exp(x); if(m==0) M(x,y) else L(x,y);}
fprintf(o,"1 setlinecap 1 setlinejoin .012 W 0 0 .4 RGB S\n");
x=-.55; y=log(M_E-1.)+x; M(x,y)
x=4; y=log(M_E-1.)+x; L(x,y)
fprintf(o,".012 W .5 0 0 RGB S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
    system("epstopdf ShokoPlotA.eps");
    system(    "open ShokoPlotA.pdf");            
    getchar(); system("killall Preview");//for mac
}

// Copyleft 2012 by Dmitrii Kouznetsov

Latex generator of labels

% FIle ShokoPlotA.pdf sould be generated with the code above in order to compile the Latex document below.

% \documentclass[12pt]{article} %<br> \usepackage{geometry} %<br> \usepackage{graphics} %<br> \usepackage{rotating} %<br> \paperwidth 804pt %<br> \paperheight 460pt %<br> \topmargin -111pt %<br> \oddsidemargin -73pt %<br> \parindent 0pt %<br> \pagestyle{empty} %<br> \newcommand \sx {\scalebox} %<br> \newcommand \rot {\begin{rotate}} %<br> \newcommand \ero {\end{rotate}} %<br> \begin{document} %<br> \begin{picture}(802,462) %<br> \put(0,0){\includegraphics{ShokoPlotA}} %<br> \put(380,432){\sx{3}{$y$}} %<br> \put(380,392){\sx{3}{$4$}} %<br> \put(380,292){\sx{3}{$3$}} %<br> \put(380,192){\sx{3}{$2$}} %<br> \put(380, 92){\sx{3}{$1$}} %<br> \put( 75, 3){\sx{3}{$-\!3$}} %<br> \put(175, 3){\sx{3}{$-\!2$}} %<br> \put(275, 3){\sx{3}{$-\!1$}} %<br> \put(394, 3){\sx{3}{$0$}} %<br> \put(494, 3){\sx{3}{$1$}} %<br> \put(594, 3){\sx{3}{$2$}} %<br> \put(694, 3){\sx{3}{$3$}} %<br> \put(785, 3){\sx{3}{$x$}} %<br> \put(428,238){\sx{3.1}{\rot{72} $y\!=\!(\mathrm e\!-\!1)\mathrm e^x$\ero}} %<br> \put(416,120){\sx{3.2}{\rot{40} $y\!=\!\mathrm{Shoko}(x)$\ero}} %<br> \put(424,44){\sx{3.1}{\rot{44.8} $y\!=\!x\!+\!\ln(\mathrm e\!-\!1)$\ero}} %<br> \end{picture} %<br> \end{document} %<br> %

% Copyleft 2012 by Dmitrii Kouznetsov