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Summation of sin

  1. Apr 2, 2007 #1
    Can anyone give some hints on how to solve this:

    [tex]\sum_{n=0}^{K-1}\frac{sin(2\pi n^2\Delta)}{n}[/tex]

    It's just the n^2 that complicates things. I tried re-writing it as

    [tex]Im\sum_{n=0}^{K-1}\frac{e^{j n^2 x}}{n}[/tex],

    where [tex]x=2\pi \Delta[/tex]
    but I cannot solve this either.

    Last edited: Apr 2, 2007
  2. jcsd
  3. Apr 2, 2007 #2
    What is delta? If it is an integer than sin(2*pi*k) for any integer k is equal to 0.
  4. Apr 2, 2007 #3
    Thanks for the reply.

    Delta is a number between (0, 1(.
    BTW, K will later be taken to infinity if that makes a difference.
  5. Apr 2, 2007 #4
    Perhaps some well choosen function which has poles at certain places in the complex plane to give that summation as residues might be useful? Then you can use a contour integral and Jordans lemma to turn that sum into an integral along the Reals somehow?

    That's without putting pen to paper so I might be way off.
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