summation of sin

svensl

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

d_leet

What is delta? If it is an integer than sin(2*pi*k) for any integer k is equal to 0.

svensl

Thanks for the reply.

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

AlphaNumeric

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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svensl	summation of sin 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

d_leet	What is delta? If it is an integer than sin(2pik) for any integer k is equal to 0.

AlphaNumeric	summation of sin 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.