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Convergence of fourier series

  1. Sep 30, 2007 #1


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

    Is that correct?
  2. jcsd
  3. Sep 30, 2007 #2


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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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