# Convergence of fourier series

1. Sep 30, 2007

### malawi_glenn

1. The problem statement, all variables and given/known data

Write f(t) = 1 + t as fourier series, with only cosine terms in the interval [0,pi]

For which values of t does the series converge to f ?

3. The attempt at a solution

Expand f = 1+t as an even function about t=0; so it will be a zig-zag with non continous points at -pi,0,pi, 2pi etc

the first part is simple, but the second; I was thinking that the Fourier series is converging to f, exept where f is not continous. So the answer is $$t \in ]0,\pi[$$

Is that correct?

2. Sep 30, 2007

### Dick

Yes. In fact it converges to 1+pi/2 at 0 and pi which is not the same as f.