function fouriersmooth
% Fourier coefficients for a smooth function
kmax = 20;
f = zeros(kmax+1,1);
f(1) = abs(quadgk(@(x)mycos(x,0),0,2*pi));
for k = 1:kmax,
   f1 = quadgk(@(x)mysin(x,k),0,2*pi);
   f2 = quadgk(@(x)mycos(x,k),0,2*pi);
   f(k+1) = sqrt(f1^2+f2^2); 
end
semilogy(0:kmax,f),
makelarge
xlabel('k');
title('Fourier coefficients of smooth function');


function y = mysin(x,k)
y = exp(cos(x)) .* sin(k*x);

function y = mycos(x,k)
y = exp(cos(x)) .* cos(k*x);