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Old 2020-03-17, 12:45   #1
wildrabbitt
 
Jul 2014

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Default something about a sum

Hi, can anyone explain this?



\[S=\sum_{v=-\infty}^{\infty}\int_0^Ne^{2\pi ivx+2\pi i\frac{x^2}{N}} \mathrm{d}x\]
\[=N\sum_{v=-\infty}^{\infty}\int_0^1e^{2\pi iN(x^2+vx)} \mathrm{d}x\]


What I'm hoping for is some intermediate steps which get from the first, step by step to the second that make sense.


Please help.

Last fiddled with by wildrabbitt on 2020-03-17 at 12:53
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