File:Facsma.jpg

Explicit plot of Factorial,

$y=\mathrm{Factorial}(x)=x!$

C++ generator of curve
//#define std::z_type complex typedef std::complex z_type; DB expaunoc[31]= {1., 0.5772156649015329,   -0.6558780715202537,     -0.04200263503409518,    0.16653861138229112, -0.04219773455554465,   -0.009621971527877027,   0.0072189432466631676, -0.0011651675918590183, -0.0002152416741149077,  0.00012805028238804805,-0.00002013485478102872,-1.2504934818746705e-6, 1.1330272320364543e-6, -2.0563384228733383e-7, 6.1160952968819515e-9,  5.00200766282674e-9, -1.1812748557105124e-9, 1.0434320074637071e-10, 7.782441358017422e-12, -3.696820627396846e-12, 5.10702591327572e-13, -2.0650148258027912e-14,-6.217248937900877e-15,  7.771561172376096e-16, -9.992007221626409e-16, -3.3306690738754696e-16, 5.551115123125783e-16, -1.1102230246251565e-16, 1.3322676295501878e-15, 9.992007221626409e-16 }; z_type expauno(z_type z) {int n,m; DB x,y; z_type s; s=expaunoc[24]; x=Re(z);if(x<-.9) return expauno(z+1.)-log(z+1.); if(x>.5) return expauno(z-1.)+log(z); y=Im(z); if(fabs(y)>.7)return expauno(z/2.)+expauno(z/2.-.5)+z*log(2.)-log(sqrt(M_PI)); for(n=23; n>=0; n--) { s*=z;s+=expaunoc[n]; }                  return -log(s); } z_type fracti(z_type z){ z_type s; int n; DB a[17]= {0.0833333333333333333, 0.0333333333333333333, .252380952380952381, .525606469002695418,  1.01152306812684171,   1.51747364915328740,   2.26948897420495996, 3.00991738325939817,  4.02688719234390123,   5.00276808075403005,   6.28391137081578218, 7.49591912238403393,  9.04066023436772670,  10.4893036545094823,   12.2971936103862059, 13.9828769539924302, 16.0535514167049355 }; /* a[0]=1./12.; a[1]=1./30.; a[2]=53./210.; a[3]=195./371.; a[4]=22999./22737.; a[5]=29944523./19773142.; a[6]=109535241009./48264275462.; a[7]=29404527905795295658./9769214287853155785.; a[8]=455377030420113432210116914702./113084128923675014537885725485.; a[9]=26370812569397719001931992945645578779849./5271244267917980801966553649147604697542.; a[10]=152537496709054809881638897472985990866753853122697839./24274291553105128438297398108902195365373879212227726.; a[11]= too long... */ s=a[16]/(z+19./(z+25./(z))); for(n=15;n>=0;n--) s=a[n]/(z+s); return s + log(2.*M_PI)/2. - z + (z+.5)*log(z); } z_type lofac(z_type z){DB x,y,r; x=Re(z); y=Im(z); if(fabs(y)>5 ) return fracti(z); if(x>0 && (x-3)*(x-3.)+y*y >25) return fracti(z); return expauno(z); } void ado(FILE *O, int x, int y, int X, int Y) {      fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%'); fprintf(O,"%c%cBoundingBox: %d %d %d %d\n",'%','%',x,y,X,Y); fprintf(O,"/M {moveto} bind def\n"); fprintf(O,"/L {lineto} bind def\n"); fprintf(O,"/S {stroke} bind def\n"); fprintf(O,"/s {show newpath} bind def\n"); fprintf(O,"/C {closepath} bind def\n"); fprintf(O,"/F {fill} bind def\n"); fprintf(O,"/times-Roman findfont 20 scalefont setfont\n"); fprintf(O,"/W {setlinewidth} bind def\n"); fprintf(O,"/RGB {setrgbcolor} bind def\n");}
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 6) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)

int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; //FILE *o;o=fopen("FactoReal.eps","w");ado(o,0,0,98,144); //FILE *o;o=fopen("facplo.eps","w");ado(o,0,0,98,144); FILE *o;o=fopen("facsmall.eps","w");ado(o,0,0,460,1100); fprintf(o,"110 10 translate\n 100 100 scale\n"); for(m=-1;m<4;m++) { if(m==0) {M(m,0)L(m,7)} else {M(m,0)L(m,6)}} for(n=0;n<7;n++) {     M( -1,n)L(3,n)} fprintf(o,".006 W 0 0 0 RGB S\n"); //     DO(m,24){x=-3.9744+.03933*m; z=x; y=Re(fac(z)); if(m==0)M(x,y) else L(x,y);} //     DO(m,21){x=-2.921+.039*m; z=x; y=Re(fac(z)); if(m==0)M(x,y) else L(x,y);} //     DO(m,20){x=-1.832+.0347*m; z=x; y=Re(fac(z)); if(m==0)M(x,y) else L(x,y);} //     DO(m,41){x=-0.866+.0999*m; z=x; y=Re(fac(z)); if(m==0)M(x,y) else L(x,y);} DO(m,45){x=-0.914+.1*m; z=x; y=Re(fac(z)); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinejoin 1 setlinecap .04 W 1 0 0 RGB S\n"); fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf facsmall.eps"); system("open facsmall.pdf"); //for macintosh getchar; system("killall Preview"); //for macintosh }
 * 1) define fac(z) exp(lofac(z))
 * 1) define M(x,y) fprintf(o,"%8.5f %8.5f M\n",0.+x, 0.+y);
 * 2) define L(x,y) fprintf(o,"%8.5f %8.5f L\n",0.+x, 0.+y);

Latex generator of labels
\documentclass[12pt]{article} \paperwidth 470pt \paperheight 1140pt \textwidth 1800pt \textheight 1800pt \topmargin -108pt \oddsidemargin -78pt \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}(686,1106) %\put(0,0) {\ing{facit}} \put(0,0) {\ing{facsmall}} \put(84,686){\sx{4.1}{$y$}} \put(84,596){\sx{4}{$6$}} \put(84,496){\sx{4}{$5$}} \put(84,396){\sx{4}{$4$}} \put(84,296){\sx{4}{$3$}} \put(84,196){\sx{4}{$2$}} \put(84, 96){\sx{4}{$1$}} \put(98,-30){\sx{4}{$0$}} \put(198,-30){\sx{4}{$1$}} \put(298,-30){\sx{4}{$2$}} \put(398,-30){\sx{4}{$3$}} \put(448,-30){\sx{4.1}{$x$}} \put(400,640){\sx{4.2}{\rot{84}$y\!=\!\mathrm{Factorial}(x)$\ero}} \end{picture} \end{document}