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Complex form of Fourier series

  1. Jul 5, 2010 #1
    Though I can compute the coefficients of Trigonometric form of Fourier series, how can I compute the coefficients of complex form of Fourier series.
     
  2. jcsd
  3. Jul 5, 2010 #2
    I assume you mean on the form e^ix? Or am I on the wrong track here?

    If my assumption is correct you want to write your function on the form
    [tex]f(x) = \sum_{-\infty}^{\infty}c_ke^{inx}[/tex]

    If so, the Fourier coefficents are given by

    [tex]c_k = \frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)e^{-inx}[/tex]
     
  4. Jul 5, 2010 #3

    mathman

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    Since you know how to compute Fourier series using sine and cosine, just use the identity:
    e-inx=cos(nx)-isin(nx).
     
  5. Jul 5, 2010 #4
    Have you guys got any links where there is proof of derivation of complex fourier series?
     
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