## summation of sin

Hello,
Can anyone give some hints on how to solve this:

$$\sum_{n=0}^{K-1}\frac{sin(2\pi n^2\Delta)}{n}$$

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

$$Im\sum_{n=0}^{K-1}\frac{e^{j n^2 x}}{n}$$,

where $$x=2\pi \Delta$$
but I cannot solve this either.

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

## 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.

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