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Fourier Series Coefficients

  1. Mar 13, 2009 #1

    I'm trying to find out what conditions need to be satisfied in order to prove that this particular function is continuous:

    f(t) = Exp[-it/2] * Sum[a(n)*Conjugate[a(n-1)]*Exp[-in]]

    where the sum is taken over n from minus infinity to infinity and a(n) is the fourier coefficient of some periodic function, calculated by
    a(n) = 1/2pi * Integrate[f(x)*Exp[-i*n*x]], integrated in x over a 2pi period

    As Exp[in] and Exp[it/2] are both continuous, I think the the answer lies in the a(n), but proving this is tricky. Any help would be really really appreciated.

    Thanks so much,

  2. jcsd
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