Please take a look at the lowest equation in this picture:
This is Parselvals Identity.
Let us say that I am given a Fourier series of f(x), and I want to calculate the integral of f(x)^2 from -L to L. In order to do this, I use Parsevals Identity. But the requirement for me to use Parsevals Identity is that the series is well-defined and square integrable. How do I show this?
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