File:Sufact.png

Explicit plot of functions Factorial and SuFac:

$y=x! ~$ and $~y=\mathrm{SuFac}(x)$ versus $x$.

This is adaptation of Figure 8.4 from the Russian book "Superfunctions" (Суперфункции, in Russian) .

C++ generator of curves
Files ado.cin, fac.cin, sufac.cin should be loaded in ordert o compile the code below

//using namespace std; typedef std::complex z_type; // #include "superfactorial.cin" //#include "doya.cin" //DB Shoko(DB x) { return log(1.+exp(x)*(M_E-1.)); }
 * 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.)
 * 4) include "ado.cin"
 * 5) include "fac.cin"
 * 6) include "sufac.cin"

int main{ int m,n; double x,y; FILE *o; //o=fopen("SuperFacPlot.eps","w"); ado(o,802,1010); o=fopen("superfacplo.eps","w"); ado(o,802,1010); fprintf(o,"401 1 translate 100 100 scale\n"); for(m=-4;m<5;m++) {M(m,0)L(m,10)} for(m=0;m<11;m++) {M(-4,m)L(4,m)} fprintf(o,"2 setlinecap .01 W S\n 1 setlinecap 1 setlinejoin\n"); for(m=0;m<42;m++){x=-.5+.1*m; y=Re(fac(x));   if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W .7 0 0 RGB S\n"); for(m=0;m<54;m++){x=-4+.1*m; y=Re(superfac(x));if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W 0 0 .7 RGB S\n"); fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf superfacplo.eps"); system(   "open superfacplo.pdf"); getchar; system("killall Preview");//for mac }
 * 1) define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
 * 2) define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);

Latex generator of labels
\documentclass[12pt]{article} \paperwidth 808pt \paperheight 1056pt \textwidth 1800pt \textheight 1800pt \topmargin -108pt \oddsidemargin -72pt \parindent 0pt \pagestyle{empty} \usepackage {graphics} \usepackage{rotating} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \newcommand \sx {\scalebox} \begin{document} \begin{picture}(602,1010) %\put(0,0){\includegraphics{SuperFacPlot}} \put(0,0){\includegraphics{superfacplo}} \put(372,978){\sx{4.5}{$y$}} \put(372,890){\sx{4.5}{$9$}} \put(372,790){\sx{4.5}{$8$}} \put(372,690){\sx{4.5}{$7$}} \put(372,590){\sx{4.5}{$6$}} \put(372,490){\sx{4.5}{$5$}} \put(372,390){\sx{4.5}{$4$}} \put(372,290){\sx{4.5}{$3$}} \put(372,190){\sx{4.5}{$2$}} \put(372,90){\sx{4.5}{$1$}} \put( 066,-42){\sx{4.5}{$-\!3$}} \put(166,-42){\sx{4.5}{$-\!2$}} \put(266,-42){\sx{4.5}{$-\!1$}} \put(391,-42){\sx{4.5}{$0$}} \put(491,-42){\sx{4.5}{$1$}} \put(591,-42){\sx{4.5}{$2$}} \put(691,-42){\sx{4.5}{$3$}} \put(777,-42){\sx{4.5}{$x$}} %\put(532,440){\sx{5}{\rot{83}$y\!=\!\mathrm{SuperFactorial}(x)$\ero}} \put(532,440){\sx{5}{\rot{83}$y\!=\!\mathrm{SuFac}(x)$\ero}} %\put(660,450){\sx{4}{\rot{83}$y\!=\!\mathrm{Factorial}(x)$\ero}} % \put(740,500){\sx{5}{\rot{83}$y\!=\!\mathrm{Factorial}(x)$\ero}} \end{picture} \end{document}