Quote:
Originally Posted by wildrabbitt
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