File:E1e14z600.jpg

From TORI
Jump to: navigation, search
Original file ‎(3,566 × 6,300 pixels, file size: 1.85 MB, MIME type: image/jpeg)

Iterates of exponent to various bases $b$.

$y=\exp_b^n(x)$

for various $n$ at

$b=\mathrm e$, top plot,

$b=\eta=\exp(1/\mathrm r)$, intermediate pllot,

$b=\sqrt{2}$, bottom plot.

C++ generator of map for $b\!=\!\mathrm e$


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex>
//#define z_type complex<double>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)

//b=10
//#include "f4ten.cin"

//b=r=2.71
#include "fsexp.cin"
#include "fslog.cin"

//b=2
//#include "f2.cin"

//b=3/2=1.5
//#include "F15.cin"

//b=exp(1/e)=1.44...
//#include "e1etf.cin"

//b=sqrt(2)=1.41...
//#include "f21E.cin"

#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;

FILE *o;o=fopen("e1e14az.eps","w");ado(o,1420,820);
fprintf(o,"410 210 translate\n 100 100 scale\n");

for(m=-4;m<11;m++){M(m,-2)L(m,6)}
for(n=-2;n<7;n++){M(-4,n)L(10,n)}
fprintf(o,"0 0 0 RGB .004 W S\n");

fprintf(o,"1 setlinecap 1 setlinejoin\n");

k=0;for(m=-40;m<101;m+=1){x=.1*m;z=x;c=exp(exp(z));y=Re(c); if(k==0)M(x,y)else L(x,y);k++; if(y>6)break;}
fprintf(o,"0 0 0 RGB .01 W S\n"); //BLACK

k=0;for(m=-40;m<101;m+=1){ x=.1*m;y=exp(x); if(k==0)M(x,y) else L(x,y); k++; if(y>6)break;}
fprintf(o,"0 0 0 RGB .01 W S\n"); //BLACK

k=0;for(m=-40;m<101;m+=2){x=.1*m;z=x;c=FSEXP(.9+FSLOG(z)); y=Re(c); if(k==0)M(x,y) else L(x,y); k++;if(y>6)break;}
fprintf(o,"0 0 .8 RGB .02 W S\n"); //BLUE

k=0;for(m=0;m<141;m+=2){x=-4.+.098*m;z=x;c=FSEXP(.5+FSLOG(z)); y=Re(c); if(k==0)M(x,y) else L(x,y); k++;if(y>6)break;}
fprintf(o,"0 .7 0 RGB .02 W S\n"); // green

k=0;for(m=-40;m<101;m+=2) {x=.1*m;z=x;c=FSEXP(.1+FSLOG(z)); y=Re(c); if(k==0)M(x,y) else L(x,y); k++;if(y>6)break;}
fprintf(o,".8 0 0 RGB .02 W S\n"); //RED

M(-2,-2)L(6.1,6.1) fprintf(o,"0 0 0 RGB .01 W S\n"); // BLACK

DO(m,82){x=-2.1+.1*m;z=x;c=FSEXP(.1+FSLOG(z));y=Re(c);if(m==0)M(y,x) else L(y,x);}
fprintf(o,".8 0 0 RGB .02 W S\n"); //RED

DO(m,64){x=-2.1+.1*m;z=x;c=FSEXP(.5+FSLOG(z));y=Re(c);if(m==0)M(y,x) else L(y,x);}
fprintf(o,"0 .7 0 RGB .02 W S\n"); // green

DO(m,48){x=-2.1+.1*m;z=x;c=FSEXP(.9+FSLOG(z));y=Re(c);if(m==0)M(y,x) else L(y,x);}
fprintf(o,"0 0 .8 RGB .02 W S\n"); //BLUE

DO(m,48){x=-2.1 +.094*m;z=x;c=exp(z);y=Re(c); if(m==0)M(y,x)else L(y,x);k++;}
fprintf(o,"0 0 0 RGB .01 W S\n"); //black

DO(m,33){x=-2.1+.092*m;z=x;c=exp(exp(z));y=Re(c); if(m==0)M(y,x)else L(y,x);}
fprintf(o,"0 0 0 RGB .01 W S\n"); //black


fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
        system("epstopdf e1e14az.eps");
        system( "open e1e14az.pdf"); //for macintosh
// getchar(); system("killall Preview"); //for macintosh
}

C++ generator of map for $b\!=\!\eta=\exp(1/\mathrm e)$


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex>
//#define z_type complex<double>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)

//b=10
//#include "f4ten.cin"

//b=r=2.71
//#include "fsexp.cin"
//#include "fslog.cin"

//b=2
//#include "f2.cin"

//b=3/2=1.5
//#include "F15.cin"

//b=exp(1/e)=1.44...
#include "e1etf.cin"
#include "e1eti.cin"
#include "e1egf.cin"
#include "e1egi.cin"


//b=sqrt(2)=1.41...
//#include "f21E.cin"

#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;

FILE *o;o=fopen("e1e14bz.eps","w");ado(o,1420,820);
fprintf(o,"410 210 translate\n 100 100 scale\n");

for(m=-4;m<11;m++){M(m,-2)L(m,6)}
for(n=-2;n<7;n++){M(-4,n)L(10,n)}
M(M_E,0)L(M_E,M_E)L(0,M_E)
fprintf(o,"0 0 0 RGB .004 W S\n");

fprintf(o,"1 setlinecap 1 setlinejoin\n");

DO(m,84){x=-4.+.1004*m;z=x;c=exp(exp(z/M_E)/M_E);y=Re(c); if(m==0)M(x,y)else L(x,y);}
fprintf(o,"0 0 0 RGB .01 W S\n"); //BLACK

DO(m,90){ x=-4.+.1003*m;y=exp(x/M_E); if(m==0)M(x,y) else L(x,y);}
fprintf(o,"0 0 0 RGB .01 W S\n"); //BLACK

DO(m,74){ x=M_E+.1*(m+.5); z=x; c=E1EGF(.9+E1EGI(z));y=Re(c);if(m==0)M(x,y) else L(x,y); if(y>6)break;}
DO(m,66){ x=M_E-.103*(m+.5); z=x; c=E1ETF(.9+E1ETI(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y);}
fprintf(o,"0 0 .8 RGB .02 W S\n"); //BLUE

DO(m,74){ x=M_E+.1*(m+.5); z=x; c=E1EGF(.5+E1EGI(z)); y=Re(c); if(m==0)M(x,y) else L(x,y); if(y>6)break;}
DO(m,66){ x=M_E-.103*(m+.5); z=x; c=E1ETF(.5+E1ETI(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y); if(y<-2)break;}
fprintf(o,"0 .7 0 RGB .02 W S\n"); //GREEN

DO(m,74){ x=M_E+.1*(m+.5); z=x; c=E1EGF(.1+E1EGI(z)); y=Re(c); if(m==0)M(x,y) else L(x,y); if(y>6)break;}
DO(m,66){ x=M_E-.1*(m+.5); z=x; c=E1ETF(.1+E1ETI(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y); if(y<-2)break;}
fprintf(o,".8 0 0 RGB .02 W S\n"); //RED

M(-2,-2)L(6,6) fprintf(o,"0 0 0 RGB .01 W S\n"); // BLACK

DO(m,74){ x=M_E+.1*(m+.5); z=x; c=E1EGF(-.1+E1EGI(z)); y=Re(c); if(m==0)M(x,y) else L(x,y); if(y>6)break;}
DO(m,42){ x=M_E-.103*(m+.5); z=x; c=E1ETF(-.1+E1ETI(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y);}
fprintf(o,".8 0 0 RGB .02 W S\n"); //RED

DO(m,74){ x=M_E+.1*(m+.5); z=x; c=E1EGF(-.5+E1EGI(z)); y=Re(c); if(m==0)M(x,y) else L(x,y); if(y>6)break;}
DO(m,66){ x=M_E-.066*(m+.5); z=x; c=E1ETF(-.5+E1ETI(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y); if(y<-2)break;}
fprintf(o,"0 .7 0 RGB .02 W S\n"); //GREEN

DO(m,74){ x=M_E+.1*(m+.5); z=x; c=E1EGF(-.9+E1EGI(z)); y=Re(c); if(m==0)M(x,y) else L(x,y); if(y>6)break;}
DO(m,52){ x=M_E-.046*(m+.5); z=x; c=E1ETF(-.9+E1ETI(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y);}
fprintf(o,"0 0 .8 RGB .02 W S\n"); //BLUE

DO(m,89){ x=.4+.1*(m+.5); z=x; c=log(z)*M_E; y=Re(c); if(m==0)M(x,y) else L(x,y);}
DO(m,89){ x=1.14+.1*(m+.5); z=x; c=log(log(z)*M_E)*M_E; y=Re(c); if(m==0)M(x,y) else L(x,y);}
fprintf(o,"0 0 0 RGB .02 W S\n"); //Black

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
        system("epstopdf e1e14bz.eps");
        system( "open e1e14bz.pdf"); //for macintosh
        getchar(); system("killall Preview"); //for macintosh
}

C++ generator of map for $b\!=\!\sqrt{2}$


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex>
//#define z_type complex<double>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)

//b=10
//#include "f4ten.cin"

//b=r=2.71
//#include "fsexp.cin"
//#include "fslog.cin"

//b=2
//#include "f2.cin"

//b=3/2=1.5
//#include "F15.cin"

//b=exp(1/e)=1.44...
//#include "e1etf.cin"
//#include "e1eti.cin"
//#include "e1egf.cin"
//#include "e1egi.cin"

//b=sqrt(2)=1.41...
#include "sqrt2f21e.cin"
#include "sqrt2f21l.cin"
//#include "f23E.cin"
//#include "f23L.cin"
//#include "f43E.cin"
//#include "f43L.cin"
#include "sqrt2f45e.cin"
#include "sqrt2f45l.cin"

#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;

FILE *o;o=fopen("e1e14cz.eps","w");ado(o,1420,820);
fprintf(o,"410 210 translate\n 100 100 scale\n");

for(m=-4;m<11;m++){M(m,-2)L(m,6)}
for(n=-2;n<7;n++){M(-4,n)L(10,n)}
//M(M_E,0)L(M_E,M_E)L(0,M_E)
fprintf(o,"0 0 0 RGB .004 W S\n");

fprintf(o,"1 setlinecap 1 setlinejoin\n");
q=log(2.)/2.;

M(-2.1,-2.1)L(6.1,6.1)
fprintf(o,"0 0 0 RGB .003 W S\n"); //BLACK

DO(m, 89){x=-4.+.0995*m;z=x;c=exp(exp(z*q)*q);y=Re(c); if(m==0)M(x,y)else L(x,y)}
DO(m,93){x=-4+.1*m;y=exp(x*q); if(m==0)M(x,y) else L(x,y);}
DO(m, 76){x=-2.+.0995*m;z=x;c=exp(exp(z*q)*q);y=Re(c); if(m==0)M(y,x)else L(y,x)}
DO(m, 82){x=-2+.0994*m;y=exp(x*q); if(m==0)M(y,x) else L(y,x);}
fprintf(o,"0 0 0 RGB .005 W S\n"); //BLACK

DO(m,66){ x=4. - .123*(m+.5); z=x; c=F21E(.9+F21L(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y);}
fprintf(o,"0 0 .8 RGB .03 W S\n"); //BLUE

DO(m,33){ x=2. + .1*(m+.5); z=x; c=F45E(.9+F45L(z));y=Re(c);if(m==0)M(x,y) else L(x,y); }
fprintf(o,"0 0 .4 RGB .01 W S\n"); //BLUE //ok

DO(m,66){ x=4. - .123*(m+.5); z=x; c=F21E(.5+F21L(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y);}
fprintf(o,"0 .8 0 RGB .03 W S\n"); //GREEN DASH

DO(m,36){ x=2.+.1*(m+.5); z=x; c=F45E(.5+F45L(z));y=Re(c);if(m==0)M(x,y) else L(x,y);}
fprintf(o,"0 .4 0 RGB .01 W S\n"); //GREEN DARK //ok

DO(m,56){ x=4.-.123*(m+.5); z=x; c=F21E(.1+F21L(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y); }
fprintf(o,".8 0 0 RGB .03 W S\n"); //RED DASH // ok

DO(m,41){ x=2.+.1*(m+.5); z=x; c=F45E(.1+F45L(z));y=Re(c);if(m==0)M(x,y) else L(x,y); }
fprintf(o,".4 0 0 RGB .01 W S\n"); //RED DARK //ok

DO(m,46){ x=4.-.12*(m+.5); z=x; c=F21E(-.1+F21L(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y); }
fprintf(o,".8 0 0 RGB .03 W S\n"); //RED DASH bottom

DO(m,44){ x=2.+.1*(m+.5); z=x; c=F45E(-.1+F45L(z));y=Re(c);if(m==0)M(x,y) else L(x,y); }
fprintf(o,".4 0 0 RGB .01 W S\n"); //RED dark

DO(m,36){ x=4.-.12*(m+.5); z=x; c=F21E(-.5+F21L(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y); }
fprintf(o,"0 .8 0 RGB .03 W S\n"); //GREEN DASH //ok

DO(m,49){ x=2.+.1*(m+.5); z=x; c=F45E(-.5+F45L(z));y=Re(c);if(m==0)M(x,y) else L(x,y); }
fprintf(o,"0 .4 0 RGB .01 W S\n"); //GREEN DARK //ok

DO(m,42){ x=4.-.0872*(m+.5); z=x; c=F21E(-.9+F21L(z));y=Re(c);if(m/2*2==m)M(x,y) else L(x,y); }
fprintf(o,"0 0 .8 RGB .03 W S\n"); //BLUE DASH

DO(m,60){ x=2.+.1*(m+.5); z=x; c=F45E(-.9+F45L(z));y=Re(c);if(m==0)M(x,y) else L(x,y); }
fprintf(o,"0 0 .4 RGB .01 W S\n"); //BLUE DARK

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
        system("epstopdf e1e14cz.eps");
        system( "open e1e14cz.pdf"); //for macintosh
        getchar(); system("killall Preview"); //for macintosh
}

Latex generator of labels


\documentclass[12pt]{article}
%\paperwidth 472px
%\paperheight 800px
\paperwidth 428px
\paperheight 756px
\textwidth 704px
\textheight 900px
\topmargin -120px
\oddsidemargin -72px
\usepackage{graphics}
\usepackage{rotating}
\usepackage[usenames]{color}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\newcommand \rmi {\mathrm{i}}
\parindent 0pt
\pagestyle{empty}
\begin{document}
\newcommand \scalr {
\put(370,766){\sx{6}{$y$}}
\put(370,583){\sx{6}{$4$}}
\put(370,383){\sx{6}{$2$}}
\put(370,183){\sx{6}{$0$}}
\put( 600,150){\sx{6}{$2$}}
\put( 799,150){\sx{6}{$4$}}
\put( 998,150){\sx{6}{$6$}}
\put(1198,150){\sx{6}{$8$}}
\put(1380,150){\sx{6}{$x$}}
}
\sx{.3}{\begin{picture}(1400,850)
\put(0,-10){\ing{e1e14az}}\scalr
\put(0,620){\sx{10}{ \color{white}{\rule{24pt}{12pt}} }}
\put(10,640){\sx{10}{ $b\!=\!\mathrm e$}}
\put( 810,666){\rot{51}\sx{4.4}{$n\!=\!0.1$}\ero}
\put( 925,696){\rot{45}\sx{4.8}{$n\!=\!0$}\ero}
\put( 934,600){\rot{37}\sx{4.4}{$n\!=\!-0.1$}\ero}
\put(1230,570){\rot{16}\sx{4.4}{$n\!=\!-0.5$}\ero}%
\put(1220,436){\rot{8}\sx{4.5}{$n\!=\!-0.9$}\ero}%
\put(1222,374){\rot{ 6}\sx{4.6}{$n\!=\!-1$}\ero}%
\put(1230,230){\rot{ 4}\sx{4.6}{$n\!=\!-2$}\ero}
\put(446,525){\rot{81}\sx{4.3}{$y\!=\!\exp(\mathrm e^x)$}\ero}
\put(499,485){\rot{75}\sx{4.4}{$y\!=\!\exp(x)$}\ero}
\put(595,485){\rot{67}\sx{4.4}{$y\!=\!\sqrt{\exp}(x)$}\ero}
\put(840,426){\rot{19}\sx{4.6}{$y\!=\!\sqrt{\ln}(x)$}\ero}
\put(890,330){\rot{ 8}\sx{4.6}{$y\!=\!\ln(x)$}\ero}
\put(890,232){\rot{ 6}\sx{4.6}{$y\!=\!\ln(\ln(x))$}\ero}
\put(14,315){\rot{1}\sx{4.8}{$n\!=\!2$}\ero}
\put(14,210){\rot{4}\sx{4.8}{$n\!=\!1$}\ero}
\put(14,155){\rot{2}\sx{4.7}{$n\!=\!0.9$}\ero}
\put(20, 95){\rot{ 3}\sx{4.7}{$n\!=\!0.5$}\ero}
\put(234,2){\rot{45}\sx{5.5}{$y\!=\!x$}\ero}
\put(450, 0){\rot{69}\sx{4.7}{$n\!=\!-1$}\ero}
\put(550,-2){\rot{62}\sx{4.5}{$n\!=\!-2$}\ero}
\end{picture}}

\sx{.3}{\begin{picture}(1400,850)
\put(0,-10){\ing{e1e14bz}}\scalr
\put(-30,620){\sx{10}{ \color{white}{\rule{32pt}{12pt}} }}
\put(-20,640){\sx{10}{ $b\!=\!\mathrm e^{1/\mathrm e}$}}
\put( 374,456){\sx{6.5}{$\mathrm e$}}
\put( 674,158){\sx{6.5}{$\mathrm e$}}
\put( 800,680){\rot{75}\sx{4.5}{$n\!=\!2$}\ero}
\put( 846,700){\rot{63}\sx{4.3}{$n\!=\!1$}\ero}
%\put( 910,760){\rot{65}\sx{4.01}{$n\!=\!0.9$}\ero}
%\put( 940,760){\rot{58}\sx{4.01}{$n\!=\!0.5$}\ero}
%\put(1010,805){\rot{50}\sx{4.01}{$0.1$}\ero}
%\put(1050,790){\rot{45}\sx{4.01}{$-0.1$}\ero}
%\put(1090,780){\rot{25}\sx{4.3}{$n\!=\!-0.5$}\ero}
%\put(1150,760){\rot{19}\sx{4.4}{$n\!=\!-0.9$}\ero}
\put(1220,740){\rot{15}\sx{4.5}{$n\!=\!-1$}\ero}
\put(1280,650){\rot{ 7}\sx{4.5}{$n\!=\!-2$}\ero}
\put(940,630){\rot{18}\sx{4.5}{$y\!=\!\mathrm e \ln(x)$}\ero}
\put(860,560){\rot{11}\sx{4.5}{$y\!=\!\mathrm e \, \ln(\mathrm e \ln(x))$}\ero}
\put(14,318){\rot{1}\sx{5}{$n\!=\!2$}\ero}
\put(14,233){\rot{4}\sx{5}{$n\!=\!1$}\ero}
\put( 290,325){\rot{12}\sx{4}{$y\!=\!\exp(\frac{1}{\mathrm e}\mathrm e^{x/\mathrm e})$}\ero}
\put( 190,250){\rot{14}\sx{4}{$y\!=\!\exp(x/\mathrm e)$}\ero}
\put(14,177){\rot{4}\sx{5}{$n\!=\!0.9$}\ero}
\put(20, 90){\rot{15}\sx{5}{$n\!=\!0.5$}\ero}
\put(120, 0){\rot{33}\sx{5}{$n\!=\!0.1$}\ero}
%\put(220, 10){\rot{38}\sx{5.5}{$n\!=\!-0.1$}\ero}
%\put(280,-30){\rot{53}\sx{5}{$n\!=\!-0.1$}\ero}
\put(370,-8){\rot{65}\sx{4.5}{$n\!=\!-0.5$}\ero}
%\put(440,-10){\rot{75}\sx{4.5}{$n\!=\!-0.9$}\ero}
\put(498, -2){\rot{77}\sx{4.7}{$n\!=\!-1$}\ero}
\put(570,-2){\rot{82}\sx{4.9}{$n\!=\!-2$}\ero}
\end{picture}}

\sx{.3}{\begin{picture}(1400,850)
\put(0,-10){\ing{e1e14cz}}\scalr
\put(-30,620){\sx{10}{ \color{white}{\rule{32pt}{12pt}} }}
\put(-20,640){\sx{10}{ $b\!=\!\sqrt{2}$}}
\put( 848,690){\rot{73}\sx{4.5}{$n\!=\!2$}\ero}
%\put( 900,750){\rot{65}\sx{4.1}{$n\!=\!1$}\ero}
%\put( 930,760){\rot{65}\sx{4.01}{$n\!=\!0.9$}\ero}
%\put( 960,760){\rot{58}\sx{4.01}{$n\!=\!0.5$}\ero}
%\put(1025,805){\rot{50}\sx{4.01}{$0.1$}\ero}
%\put(1050,800){\rot{45}\sx{4.01}{$-0.1$}\ero}
%\put(1060,780){\rot{25}\sx{4.3}{$n\!=\!-0.5$}\ero}
%\put(1110,780){\rot{19}\sx{4.4}{$n\!=\!-0.9$}\ero}
\put(1100,728){\rot{18}\sx{4.5}{$n\!=\!-1$}\ero}
\put(1260,690){\rot{ 7}\sx{4.5}{$n\!=\!-2$}\ero}
\put( 870,600){\rot{12}\sx{4.4}{$y\!=\!\ln_b(\ln_{b}(x))$}\ero}
\put(650,480){\rot{45}\sx{5}{$n\!=\!-2$}\ero}
\put(730,435){\rot{45}\sx{5}{$n\!=\!2$}\ero}
\put(14,318){\rot{1}\sx{5}{$n\!=\!2$}\ero}
%\put(390,340){\rot{9}\sx{5}{$y\!=\!2^{\frac{1}{2} 2^{x/2} }$}\ero}
%\put(390,340){\rot{10}\sx{5}{$y\!=\!\sqrt{2}^{\sqrt{2}^x }$}\ero}
\put(14,233){\rot{4}\sx{5}{$n\!=\!1$}\ero}
%\put(220,265){\rot{5}\sx{4}{$y\!=\!2^{x/2}$}\ero}
\put(210,260){\rot{7}\sx{5}{$y\!=\!b^{x}$}\ero}
\put(14,177){\rot{4}\sx{5}{$n\!=\!0.9$}\ero}
\put(20, 90){\rot{15}\sx{5}{$n\!=\!0.5$}\ero}
\put(120, 0){\rot{33}\sx{5}{$n\!=\!0.1$}\ero}
%\put(220, 10){\rot{38}\sx{5.5}{$n\!=\!-0.1$}\ero}
%\put(280,-30){\rot{53}\sx{5}{$n\!=\!-0.1$}\ero}
\put(370,-10){\rot{65}\sx{4.5}{$n\!=\!-0.5$}\ero}
%\put(440,-10){\rot{75}\sx{4.5}{$n\!=\!-0.9$}\ero}
\put(498, 0){\rot{76}\sx{4.7}{$n\!=\!-1$}\ero}
\put(570,0){\rot{84}\sx{4.9}{$n\!=\!-2$}\ero}
\end{picture}}

\end{document}

References

http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2012-02590-7/S0025-5718-2012-02590-7.pdf http://www.ils.uec.ac.jp/~dima/PAPERS/2011e1e.pdf H.Trappmann, D.Kouznetsov. Computation of the Two Regular Super-Exponentials to base exp(1/e). Mathematics of computation, 2012 February 8. ISSN 1088-6842(e) ISSN 0025-5718(p)

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current06:11, 1 December 2018Thumbnail for version as of 06:11, 1 December 20183,566 × 6,300 (1.85 MB)Maintenance script (talk | contribs)Importing image file
  • You cannot overwrite this file.

There are no pages that link to this file.

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.
Retrieved from "https://mizugadro.mydns.jp/t/index.php?title=File:E1e14z600.jpg&oldid=18885"