%--------------------------------------------------------------------------------------
% Matlab program used to generate Fig.1
%--------------------------------------------------------------------------------------
% This program was written in May 2006 by Stan Sykora while writing
% the note on 'Exponential Transforms of Polygonal Functions',
% published online at www.ebyte.it\library\educards\math\ExpIntegralTransforms.html.
% The program is an attachment to the said article.
%--------------------------------------------------------------------------------------
% The AUTHOR hereby authorizes EVERYBODY to copy, distribute, cut, or modify
% the program in whichever form and by whatever means. If you use it and obtain
% interesting results, however, you should cite the Web article.
%
% The AUTOR DISCLAIMS any LIABILITIES which any misguided soul might claim,
% due to whatever he/she has done with the program or just thinks to have done.

clear;clc;clf;echo off;
n = 1000;
x = linspace(-5,5,n);
one = linspace(1,1,n);
zer = linspace(0,0,n);

ifreal = 0;

if ifreal
  etap = (exp(-x)-1+x)./x./x;
  etam = (exp(x)-1-x)./x./x;
  eta2 = (exp(x)+exp(-x)-2)./x./x;
  plot(x,etap,'-k','LineWidth',2,'Color',[0,0,0.5]);
  hold on;
  plot(x,etam,'-k','LineWidth',2,'Color',[0,0,0.5]);
  hold on;
  plot(x,eta2,'-k','LineWidth',2,'Color',[0,0,0]);
  hold on;
  plot(x,one,'-k','LineWidth',1,'Color',[0,0,0]);
  hold on;
else
  etap = ((1-cos(x))+i*(sin(x)-x))./x./x;
  etam = ((1-cos(x))-i*(sin(x)-x))./x./x;
  eta2 = 2*(1-cos(x))./x./x;
  plot(x,real(etap),'-k','LineWidth',2,'Color',[0.5,0,0]);
  hold on;
  plot(x,imag(etap),'-k','LineWidth',2,'Color',[0,0.5,0]);
  hold on;
  plot(x,imag(etam),'-k','LineWidth',1,'Color',[0,0.5,0]);
  hold on;
  plot(x,real(eta2),'-k','LineWidth',2,'Color',[0,0,0.5]);
  hold on;
  plot(x,zer,'-k','LineWidth',1,'Color',[0,0,0]);
  hold on;
end

set(gcf,'Color','white');
set(gca,'FontSize',20);
set(gca,'LineWidth',2);
set(gca,'TickLength',[.02,.02]);
%axis([-15 15 -0.35 1.05]);
axis([-5 5 -0.35 1.05]);
%set(gca,'xTick',[-4,-2,0,2,4]);