File:Susinploat300.jpg

Explicit plot of function SuSin in comparison to its approximations.

Black think solid curve shows $y= \mathrm{SuSin}(x)$, this is superfunction of sin, id est, super sin.

The upper thin blue curves shows the leading term of its asymptotic expansion, $y=\sqrt{3/x}$, suggested in 2012 by Kursernas Hemsidor.

The red dashed curve shows the approximation suggested in 2012 by Thomas Curtright

$y=\exp\Big( \big(1\!-\!\sqrt{x}\big)\ln(\pi/2)\Big)$

The lowest red thin curve shows the difference between the $SuSin(x)$ and the approximation by Thomas, scaled with factor 10.

C++ generator of curves
//Files ado.cin, arcsin.cin, and susin.cin should be loaded to working directory in order to compile the code below

// using namespace std; typedef complex z_type;
 * 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.)


 * 1) include "ado.cin"
 * 2) include "arcsin.cin"
 * 3) include "susin.cin"

int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DB x0=0.; DO(m,14){y=Re(susin(z_type(1.,1.e-9)+x0))-1.; x0+=4.*y; printf("%2d %19.16f %19.16f\n",m,x0,y);} //FILE *o;o=fopen("susinplot1.eps","w"); ado(o,1002,244); //FILE *o;o=fopen("04.eps","w"); ado(o,1002,348); FILE *o;o=fopen("susinploa.eps","w"); ado(o,1002,348); fprintf(o,"1 106 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); for(m=0;m<11;m++){M(m,-1) L(m,2) } for(n=-1;n<3;n++){M( 0,n) L(10,n)} fprintf(o,".006 W 0 0 0 RGB S\n"); M(0,M_PI/2.); L(10,M_PI/2) fprintf(o,".004 W 0 0 0 RGB S\n"); fprintf(o,"1 setlinejoin 1 setlinecap\n"); DO(m,100){ x=.5+.1*m; y=sqrt(3./x); if(m==0) M(x,y) else L(x,y) ; if ( x>10.) break;} fprintf(o,".006 W 0 0 1 RGB S\n"); //M(0,M_PI/2.); fprintf(o,"1 setlinejoin 0 setlinecap\n"); DO(m,300){ x=.0001+.04*m/(1+5./(.3+m)); y=exp((1.-sqrt(x))*log(M_PI/2)); if(m/2*2==m) M(x,y) else L(x,y) ; if ( x>10.) break;} fprintf(o,".02 W 1 0 0 RGB S\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); M(0,M_PI/2.); DO(m,2002){ x=.005*(m+.3); z=z_type(x,1.e-8); c=susin(z); y=Re(c); L(x,y); printf("%8.5f %8.5f\n",x,y); } fprintf(o,".012 W 0 0 0 RGB S\n"); M(0,0); DO(m,20022){ x=.005*(m+.3); z=z_type(x,1.e-8); c=susin(z); y=exp((1.-sqrt(x))*log(M_PI/2))- Re(c); y*=10; L(x,y); printf("%8.5f %8.5f\n",x,y); if(x>10) break; } fprintf(o,".006 W 1 0 0 RGB S\n");
 * 1) define M(x,y) {fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);}
 * 2) define L(x,y) {fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);}

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

Latex generator of labels
\documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphics} \usepackage{rotating} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \paperwidth 1026pt \paperheight 345pt \topmargin -109pt \oddsidemargin -90pt \newcommand \sx {\scalebox} \pagestyle{empty} \begin{document} \begin{picture}(1016,328) %\put(20,1){\includegraphics{susinplot1}} \put(20,1){\includegraphics{susinploa}} %\put(20,1){\includegraphics{04}} \put(2,312){\sx{2.4}{$y$}} \put(-1,257){\sx{2.8}{$\frac{\pi}{2}$}} \put(2,198){\sx{2.4}{$1$}} \put(2,98){\sx{2.4}{$0$}} \put(15,-16){\sx{2.4}{$0$}} \put(115,-16){\sx{2.4}{$1$}} \put(215,-16){\sx{2.4}{$2$}} \put(315,-16){\sx{2.4}{$3$}} \put(415,-16){\sx{2.4}{$4$}} \put(516,-16){\sx{2.4}{$5$}} \put(616,-16){\sx{2.4}{$6$}} \put(717,-16){\sx{2.4}{$7$}} \put(817,-16){\sx{2.4}{$8$}} \put(917,-16){\sx{2.4}{$9$}} \put(1010,-16){\sx{2.5}{$x$}} %\put(45,134){\sx{2.5}{$y\!=\!\mathrm{SuSin}(x)$}} \put(190,246){\sx{1.8}{\rot{-12}$y\!=\! \sqrt{3/x}$\ero}} \put(190,201){\sx{1.8}{\rot{-6}$y\!=\!\mathrm{SuSin}(x)$\ero}} \put(190,176){\sx{1.8}{\rot{-6}$y\!=\!\exp((1\!-\!\sqrt{x})\ln(\pi/2))$\ero}}

\put(190,110){\sx{1.8}{\rot{-8}$y\!=\! 10\Big(\exp((1\!-\!\sqrt{x})\ln(\pi/2))-\mathrm{SuSin}(x)\Big)$\ero}} \end{picture} \end{document}