Question

I sort of invented this "identity" but I don't know how I would show that it's true, any ideas? I'll explain my reasoning in a bit if anyone's interested.

Answer 1

\[\Large \int\limits_1^N \frac{1}{N} \int\limits_1^N e^{i \frac{2 \pi }{N} kn}f(e^{i \frac{2 \pi }{N} k}x)dkdn =f(x)\]