File:AteSuFacPlotU.png

Explicit plot of combination of natural ArcTetration and SuperFactorial:

\(y=\mathrm{ate}\Big(\mathrm{SuFac}(x)\Big)\)

For comparison the line \(y=x+0.8\) is also shown.

C++

/* files ado.cin, fac.cin, SuFac.cin, fslog.cin should be loaded in order to compile the code below.*/

=#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
using namespace std;
#include <complex>
typedef complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
 #include"ado.cin"
 #define M(x,y) fprintf(o,"%6.4f %6.4f M\n",1.*(x),1.*(y));
 #define L(x,y) fprintf(o,"%6.4f %6.4f L\n",1.*(x),1.*(y));
//#include "Conrec6.cin"
#include "fac.cin"
#include "SuFac.cin"
#include "fslog.cin"
//#include "filog.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
FILE *o;o=fopen("AteSuFacPlot.eps","w");ado(o,408,408);
fprintf(o,"104 4 translate\n 100 100 scale\n");

for(m=-1;m<4;m++){M(m,0)L(m,4)}
for(n=0;n<5;n++){M(-1,n)L(3,n)}
//M(0,.8)L(3,.8) // horisontal line
M(-0.8,0)L(3,.8+3)
fprintf(o,"2 setlinecap .0012 W 0 0 0 RGB S\n");

for(m=-10;m<30;m++) {	x=.1*(m-.2);
			c=superfac(x); //SuFac
			c=FSLOG(c); // ate
			y=Re(c); if(m==-10) M(x,y) else L(x,y)
 		}
fprintf(o,".018 W 0 0 1 RGB S\n");

/*
for(m=0;m<30;m++) {	x=.1*(m-.2);
			c=superfac(x); //SuFac
			c=FSLOG(c); // ate
			y=Re(c)-x; 
			if(m==0) M(x,y) else L(x,y)
 		}
fprintf(o,".01 W 0 0 1 RGB S\n");
*/

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
     system("epstopdf AteSuFacPlot.eps"); 
     system(    "open AteSuFacPlot.pdf"); //for mac
}

Latex

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[russian]{babel}
\usepackage{geometry}
\usepackage{latexsym,amsmath,amssymb,amsbsy,graphicx}
%\usepackage{graphicx}
\usepackage{wrapfig}
\usepackage{hyperref} 
\usepackage{rotating} 
\usepackage[export]{adjustbox}
\paperwidth 440pt
\paperheight 440pt                                                                                                                                                     
\topmargin -116pt
\textheight 740pt
\oddsidemargin -66pt
\textwidth 512pt
\newcommand{\ing}{\includegraphics}
\newcommand{\sx}{\scalebox}
\newcommand{\rot}{\begin{rotate}}
\newcommand{\ero}{\end{rotate}}
\parindent 0px
\begin{document}
%\sx{.82}
{\begin{picture}(440,436)
\put(20,20){\ing{AteSuFacPlot.pdf}}
%\put(20,20){\ing{AteSuExq2plot.pdf}}
\put(3,410){\sx{2.7}{\(y\)}}
\put(3,317){\sx{2.5}{\(3\)}}
\put(3,217){\sx{2.4}{\(2\)}}
\put(3,117){\sx{2.4}{\(1\)}}
\put(3,018){\sx{2.4}{\(0\)}}
\put( 1,0){\sx{2.4}{\(-1\)}}
\put(119,0){\sx{2.4}{\(0\)}}
\put(219,0){\sx{2.4}{\(1\)}}
\put(319,0){\sx{2.4}{\(2\)}}
%\put(419,0){\sx{2.4}{\(3\)}}
%\put(519,0){\sx{2.4}{\(4\)}}
%\put(619,0){\sx{2.4}{\(5\)}}
\put(410,1){\sx{2.6}{\(x\)}}

\put(242,230){\sx{2.2}{\rot{45}\(y\!=\!x+0.8\)\ero}} 
\put(276,198){\sx{2.2}{\rot{47}\(y\!=\!\mathrm{ate}\Big(\mathrm{SuFac}(x)\Big)\)\ero}} 
%\put(438,229){\sx{2.2}{\rot{34}\(y\!=\!\mathrm{ate}\Big(\mathrm{SuExq2}(x)\Big)\)\ero}} 
%\put(556,229){\sx{2.2}{\rot{44}\(y\!=x\!-\!2\)\ero}} 
\end{picture}}
\end{document}

References

Keywords

«Abel function», «Abelfunction», «ado.cin», «Agreement», «ArcTetration», «Asymptotic», «ChatGPT», «Elementary function», «Factorial», «Fac.cin», «Restricted asymptotic», «SuperFactorial», «Superfunction», «Superfunctions»,

«ado.cin», «fslog.cin»,

«Корень из факториала», «Суперфункции»,