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Fourier question

  1. Sep 24, 2009 #1
    1. The problem statement, all variables and given/known data
    i was wondering why this is equal to zero : [tex] \int^{\pi}_{-\pi} e^{i(n+m)x }dx= 0 [/tex] when [itex] n\neq m [/itex]


    2. Relevant equations


    [tex] e^{inx} = cos(nx) + isin(nx) [/tex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Sep 24, 2009
  2. jcsd
  3. Sep 24, 2009 #2

    Dick

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    m and n are integers, right? And I think you want (n-m) in the integral if your condition is n not equal to m. Just work out the integral to see why it's zero.
     
  4. Sep 24, 2009 #3
    Yes they are integers, and thanks for the correction it should be n-m , thanks, now anyone with links to a tutorial on why, [tex] \left[ \frac {e^{2nix} } {2ni} \right]^{\pi}_{-\pi} = \pi [/tex]
     
    Last edited: Sep 24, 2009
  5. Sep 24, 2009 #4

    Dick

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    e^(i*n*pi) (where n is an integer) is +1 if n is even and -1 if n is odd. e^(-i*n*pi) is that same value. I don't think you need a tutorial to prove the difference is 0.
     
  6. Sep 24, 2009 #5
    Ok, very nice thanks
     
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