File:BesselH0mapT050.png

Complex mp of the Hankel function of zeroth order, id est, map of BesselH0 in the complex plane.

$ u+\mathrm i v = \mathrm{BesselH}[0,x+\mathrm i y]$

C++ generator of curves
// Files ado.cin, conto.cin, besselj0.cin, bessely0.cin should be loaded at the working directory in order to compile the C++ code below:

using namespace std; typedef complex z_type;
 * 1) include 
 * 2) include 
 * 3) define DB double
 * 4) 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 "conto.cin"
 * 5) include "besselj0.cin"
 * 6) include "bessely0.cin"

main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; int M=803,M1=M+1; int N=201,N1=N+1; DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array. char v[M1*N1]; // v is working array FILE *o;o=fopen("besselH0map.eps","w");ado(o,202,102); fprintf(o,"101 51 translate\n 10 10 scale\n"); /* fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.5;q=.5; fprintf(o,"0 2.5 13 -11 11 arc  .3 W .6 1 1 RGB S\n"); fprintf(o,"0 2.5 13 159 191 arc   S\n"); fprintf(o,"0 -2.5 13 -11 11 arc S\n"); fprintf(o,"0 -2.5 13 -191 -159 arc S\n"); DO(m,400) X[m]=-10.+.025*m; X[400]=-.014; X[401]=-.004; X[402]= .004; X[403]= .014; for(m=404;m<M1;m++) X[m]=-10.+.025*(m-3.); DO(n,100)Y[n]=-5.+.05*n; Y[100]=-.006; Y[101]= .006; for(n=102;n-30. && p<30.     &&     q>-30. && q<30.      ) {g[m*N1+n]=p; f[m*N1+n]=q; }                     }} //#include "plodi.cin" /* conto(o,g,w,v,X,Y,M,N,15, -p,p); fprintf(o,".07 W 1 0 1 RGB S\n"); conto(o,g,w,v,X,Y,M,N,14, -p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,13, -p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,12, -p,p); fprintf(o,".06 W 0 0 1 RGB S\n"); conto(o,g,w,v,X,Y,M,N,11, -p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,10, -p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, 9, -p,p); fprintf(o,".06 W 0 1 1 RGB S\n"); conto(o,g,w,v,X,Y,M,N, 8, -p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, 7, -p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, 6, -p,p); fprintf(o,".07 W 0 1 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, 5, -p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, 4, -p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, 3, -p,p); fprintf(o,".06 W .5 .5 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, 2, -p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, 1, -p,p); fprintf(o,".1 W 1 0 0 RGB S\n"); */ fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=2;q=.8; for(m=-10;m<10;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".016 W 0 .6 0 RGB S\n"); for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".016 W .9 0 0 RGB S\n"); for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".016 W 0 0 .9 RGB S\n"); for(m=1;m<21;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".03 W .9 0 0 RGB S\n"); for(m=1;m<21;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 .9 RGB S\n"); conto(o,f,w,v,X,Y,M,N, (0. ),-2*p,2*p); fprintf(o,".03 W .6 0 .6 RGB S\n"); for(m=-20;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n"); m=0;         conto(o,g,w,v,X,Y,M,N, (0.+m),-2*p,2*p); fprintf(o,".03 W 0 0 0 RGB S\n"); for(m=1;m<21;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n"); //#include "plofu.cin" M(0,0)L(-20,0) fprintf(o,"1 1 1 RGB 0.032 W 0 setlinecap S\n"); DO(n,80) {x=-.25*n; M(x-.10,0) L(x-.20,0)} fprintf(o,"0 0 0 RGB .04 W S\n"); fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf besselH0map.eps"); system(   "open besselH0map.pdf"); getchar; system("killall Preview");//for mac }

Latex generator of labels
% File besselH0map.pdf should be generated with the code above in order to compile the Latex document below.

% The document should be saved as BesselH0mapT.tex % The compilation gives BesselH0mapT.pdf % that file can be converted to PNG format with resolution 50 picels/inch giving the file loaded. % Copyleft 2012 by Dmitrii Kouznetsov.

% \documentclass[12pt]{article} % \paperheight 1038px % \paperwidth 2044px % \textwidth 2094px % \textheight 1200px % \topmargin -80px % \oddsidemargin -80px % \usepackage{graphics} % \usepackage{rotating} % \usepackage{color}% \newcommand \sx {\scalebox} % \newcommand \rot {\begin{rotate}} % \newcommand \ero {\end{rotate}} % \newcommand \ing {\includegraphics} % \newcommand \rmi {\mathrm{i}} % \begin{document} % \newcommand \zoomax { % \put(16,1020){\sx{4.4}{$y$}} % \put(16,930){\sx{4}{$4$}} % \put(16,830){\sx{4}{$3$}} % \put(16,730){\sx{4}{$2$}} % \put(16,630){\sx{4}{$1$}} % \put(16,530){\sx{4}{$0$}} % \put(-4, 430){\sx{4}{$-\!1$}} % \put(-4, 330){\sx{4}{$-\!2$}} % \put(-4, 230){\sx{4}{$-\!3$}} % \put(-4, 130){\sx{4}{$-\!4$}} % % \put(220, 5){\sx{4}{$-\!8$}} % \put(420, 5){\sx{4}{$-\!6$}} % \put(620, 5){\sx{4}{$-\!4$}} % \put(820, 5){\sx{4}{$-\!2$}} % \put(1043, 5){\sx{4}{$0$}} % \put(1243, 5){\sx{4}{$2$}} % \put(1443, 5){\sx{4}{$4$}} % \put(1643, 5){\sx{4}{$6$}} % \put(1843, 5){\sx{4}{$8$}} % \put(2031,6){\sx{4}{$x$}} % % } % \parindent 0pt % \begin{picture}(2016,1016) % %\put(40,30){\sx{10}{\ing{besselj1o}}} % %\put(40,30){\sx{10}{\ing{besselY0mapWide}}} % %\put(40,30){\sx{10}{\ing{besselH0small}}} % \put(40,30){\sx{10}{\ing{besselH0map}}} % \zoomax % % \put( 100,526){\sx{6}{\bf cut}} % % \put( 1070,880){\sx{5}{\rot{90}$u\!=\!0$\ero}} % \put( 1208,880){\sx{5}{\rot{90}$v\!=\!0$\ero}} %

\multiput( 182,880)(300,0){3}{\sx{5}{\rot{90}$u\!=\!0$\ero}} % \multiput( 335,880)(299,0){3}{\sx{5}{\rot{90}$v\!=\!0$\ero}} %

\multiput(1354,880)(302,0){3}{\sx{5}{\rot{90}$u\!=\!0$\ero}} % \multiput(1504,880)(300,0){3}{\sx{5}{\rot{90}$v\!=\!0$\ero}} %

\put( 264,570){\sx{3.6}{$u\!=\!-0.2$}} % \put( 426,580){\sx{3.6}{$v\!=\!-0.2$}} % \put( 590,600){\sx{3.6}{$u\!=\!0.2$}} % \put( 736,614){\sx{3.6}{$v\!=\!0.2$}} % \put( 860,652){\sx{3.6}{$u\!=\!-0.2$}} %

\put( 1106,646){\sx{3.6}{$u\!=\!0.2$}} % \put( 1234,622){\sx{3.6}{$v\!=\!0.2$}} % \put( 1370,606){\sx{3.6}{$u\!=\!-0.2$}} % \put( 1542,588){\sx{3.6}{$v\!=\!-0.2$}} % \put( 1724,570){\sx{3.6}{$u\!=\!0.2$}} % \put( 1880,564){\sx{3.6}{$v\!=\!0.2$}} %

\put( 202,494){\sx{5}{$v\!=\!0$}} % \put( 512,496){\sx{5}{$v\!=\!0$}} % \put( 820,498){\sx{5}{$v\!=\!0$}} %

\put( 455,402){\sx{5}{$v\!=\!1$}} %

\put( 780,434){\sx{5}{$v\!=\!-1$}} % \put( 780,376){\sx{5}{$v\!=\!-2$}} %

\put( 990,390){\sx{5}{$u\!=\!3$}} % \put( 990,340){\sx{5}{$u\!=\!4$}} %

\put(1198,464){\sx{5}{$v\!=\!1$}} % \put(1190,390){\sx{5}{$v\!=\!2$}} %

\end{picture} % % \end{document} % %

% % Copyleft 2012 by Dmitrii Kouznetsov

Keywords
Besselj0.cin, Bessely0.cin, ado.cin, conto.cin, BesselH0, C++, Latex, Complex map