File:CihplotT.png

Explicit plot $y=\mathrm{Cih}(x)=\cosh(x)/x$.

The minimum is realized at
 * $x=H\approx 1.199678640257734$ ;
 * $J=\mathrm{Cih}(H)\approx 1.50887956153832$

C++ generator of curve
File ado.cin should be placed to the working directory in order to vompile the C++ code below.

using namespace std; typedef complex z_type; //#include "acip.cin" main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; //DB y1= 1.1996786402577337; //DB zL= 2.798386045783887; //DB fL= -0.33650841691839534; DB Ho=1.199678640257734; DB Jo=1.50887956153832; FILE *o;o=fopen("cihplot1.eps","w");ado(o,320,271); fprintf(o,"10 -90 translate\n 100 100 scale\n"); for(m=0;m<4;m++){M(m,1)L(m,3.5)} for(n=1;n<4;n++){M(0,n)L(3,n)} fprintf(o,"2 setlinecap .008 W 0 0 0 RGB S\n"); for(m=0;m<3;m++){M(.5+m,1)L(.5+m,3.5)} for(n=1;n<4;n++){M(0,n+.5)L(3,n+.5)} fprintf(o,"2 setlinecap .003 W 0 0 0 RGB S\n"); //M(fL,zL) DO(m,274){ x=.298+.01*m; //z=x; y=Re(ACip5(z)); y=cosh(x)/x; if(m==0)M(x,y) else L(x,y) } fprintf(o,"1 setlinejoin 1 setlinecap .012 W 0 .4 0 RGB S\n"); p=1.8;q=.7; // M(fL,1)L(fL,zL) L(0,zL) fprintf(o,"2 setlinecap .003 W 0 0 0 RGB S\n"); M(Ho,1)L(Ho,Jo) L(0,Jo) fprintf(o,"2 setlinecap .003 W 0 0 0 RGB S\n"); fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf cihplot1.eps"); system(   "open cihplot1.pdf"); getchar; system("killall Preview");//for mac }
 * 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"
 * 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);
 * 3) define S(x,y) fprintf(o,"S\n",);

Latex generator of labels
FIle cihplot1.pdf should be generated with the code above in order to compile the latex document below. % Copyleft 2012 by Dmitrii Kouznetsov % \documentclass[12pt]{article} % \usepackage{geometry} % \usepackage{graphicx} % \usepackage{rotating} % \paperwidth 610pt % \paperheight 510pt % \topmargin -92pt % \oddsidemargin -106pt % \textwidth 900pt % \textheight 900pt % \pagestyle {empty} % \newcommand \sx {\scalebox} % \newcommand \rot {\begin{rotate}} % \newcommand \ero {\end{rotate}} % \newcommand \ing {\includegraphics} % \begin{document} % \parindent 0pt \sx{2}{ \begin{picture}(340,260) % %\put(4,6){\ing{acosplot}} % % \put(4,6){\ing{aciplot}} % \put(4,6){\ing{cihplot1}} % \put(16,250){\sx{1.8}{$y$}} %v \put(16,210){\sx{1.8}{\bf 3}} % \put(16,160){\sx{1.8}{\bf 2.5}} % \put(16,110){\sx{1.8}{\bf 2}} % \put(13, 68){\sx{1.8}{$J$}} % \put(12, 52){\sx{1.8}{\bf 1.5}} % %\put(58, 19){\sx{2}{\bf 0}} % \put(108, 19){\sx{2}{\bf 1}} % \put(124, 19){\sx{2}{$H$}} % \put(208, 19){\sx{2}{\bf 2}} % \put(300, 21){\sx{2.1}{$x$}} % \put(230,124){\sx{1.6}{\rot{54}$y\!=\!\mathrm{Cih}(x)$\ero}} \end{picture} % } % \end{document}