% m53_series.m - Explore Fourier and Chebyshev series with Chebfun


% FOURIER

F = chebfun('cos(exp(sin(t)))', [-pi,pi], 'trig')
subplot(1,2,1), plot(F,'.-')
subplot(1,2,2), plotcoeffs(F,'.-')
sum(F)
roots(F)

help cheb.gallerytrig


% CHEBYSHEV

f = chebfun('cos(exp(sin(x)))', [-pi,pi])
subplot(1,2,1), plot(f,'.-')
subplot(1,2,2), plotcoeffs(f,'.-')
sum(f)
roots(f)

help cheb.gallery


% "SMOOTHIES" - C-INFINITY but NOWHERE ANALYTIC

f = smoothie('trig');
subplot(1,2,1), plot(f)
subplot(1,2,2), plotcoeffs(f)

f = smoothie;
subplot(1,2,1), plot(f)
subplot(1,2,2), plotcoeffs(f)