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Math Help - Fourier series

  1. #1
    Super Member Deadstar's Avatar
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    Fourier series

    Quick Q.

    When dealing Fourier series Q's, \cos(n \pi) is written as (-1)^n. What can \cos (\frac{n \pi}{2}) be written as? I might as well write out the equation i'm trying to simplify...

    -\frac{2T}{n \pi}( 2 \cos \frac{n \pi}{2} - 1 - \cos{n \pi} ) = ?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    its either -1,0, or 1

    if n is odd it is 0

    If n is even its either -1 or 1

    So there is no simple form
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  3. #3
    Super Member Deadstar's Avatar
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    Cheers, think I've got it figured out anyway...

    It equals \frac{8T}{n \pi} whenever n is in the form 4m + 2 and 0 otherwise.
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