% m54_bernstein.m - Chebyshev series and Bernstein ellipses

f = chebfun('1./(1+25*x.^2)');

subplot(1,3,1), plot(f), ylim([-1 2])
subplot(1,3,2), plotcoeffs(f,'linewidth',.6), grid on
subplot(1,3,3), plotregion(f), xlim([-1.4 1.4]), axis equal, grid on

hold on, plot([-.2i .2i],'.r')

rho = (1+sqrt(26))/5;
kk = 0:length(f);
subplot(1,3,2), hold on, plot(kk,rho.^(-kk),'--r')