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.
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Obvious substitution. You said you knew how to make substitutions in integrals.
It is perhaps unfortunate that the variables in the integrals on both sides have the same name.