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Cn coefficient for a Fourier series

  1. Mar 1, 2012 #1
    1. The problem statement, all variables and given/known data

    I have an example were they determine the Cn coefficient for a Fourier series:

    My problem is i don't follow what happens in the following moment:

    neither am i sure how the two e^-inwt comes to be cos(nwt) in the last part.

    2. Relevant equations

    3. The attempt at a solution

    The only solution I can come up with is to reverse the limits what is obvious and then say: t=-a --> -1*t=-1*-a and then change a for -a in the limit and t for -t. However this doesn't work in other similar problems so I don't think think this is right.
  2. jcsd
  3. Mar 1, 2012 #2


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    welcome to pf!

    hi sekowe! welcome to pf! :smile:

    there's a misprint :redface:

    the first exponent in the third line should be positive

    between the second and third lines, they've substituted u = -t, du = -dt, and then renamed u as t again!

    and of course the corrected third line lets you use eix + e-ix = (cosx)/2 :wink:
  4. Mar 1, 2012 #3
    A misprint... Yeah that clears up a lot :D

    Thank you very much!
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