Summation of sin

  • Thread starter svensl
  • Start date
  • #1
5
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Hello,
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.

Thanks,
svensl
 
Last edited:

Answers and Replies

  • #2
1,074
1
What is delta? If it is an integer than sin(2*pi*k) for any integer k is equal to 0.
 
  • #3
5
0
Thanks for the reply.

Delta is a number between (0, 1(.
BTW, K will later be taken to infinity if that makes a difference.
 
  • #4
289
0
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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