Convergence of fourier series

  • #1
malawi_glenn
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Homework Statement



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 ?



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 [tex] t \in ]0,\pi[ [/tex]

Is that correct?
 

Answers and Replies

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

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