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Trignometric Polynomial complex form

  1. Sep 7, 2011 #1
    I'm trying to learn Fourier transforms by myself. I'm a bit confused about how the trignometric polynomial complex form was derived. I'm refering to this:


    Now, I haven't taken complex analysis so I only know the basics. I used Euler's formula and got that far but I'm not sure what to do next.

  2. jcsd
  3. Sep 7, 2011 #2

    [tex]\cos(nx)=\frac{e^{inx}+e^{-inx}}{2}, ~\sin(nx)=\frac{e^{inx}-e^{-inx}}{2i}[/tex]

    in the series and rearrange everything. This should give you the required form.
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