View Single Post
Old 2020-03-17, 13:19   #2
Chris Card
Chris Card's Avatar
Aug 2004

2028 Posts

Originally Posted by wildrabbitt View Post
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.
Do you know how to do integration by substitution?
If so, try setting x = Ny and rewrite the integral in terms of y instead of x.

Chris Card is offline   Reply With Quote