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Proof of Plancherel for quantum

  1. Oct 5, 2011 #1
    So, I've been asked to show that
    f(x)=Ʃn=0 [ansin(nπx/a) + bncos(nπx/a)

    is equivalent to f(x)=Ʃn=-∞ cneinx/a



    I'm kinda stuck. i want to turn this into the exponential form but I don't see how to condense this into a single term.



    Thanks!
     
  2. jcsd
  3. Oct 5, 2011 #2
    Nevermind, Solved

    Use the substitution that sinu = 0.5i (e^iu -e^-iu) and the equivalent for cosine and shift the register of the summation.
     
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