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## Main Question or Discussion Point

**When is a function "equal to" its Fourier series?**

First of all - a bit unsure where this post fits in, there seems to be no immediately appropriate subforum.

So I'm a physics student and currently looking at what it takes for a Fourier series to converge. I've looked at wiki (http://en.wikipedia.org/wiki/Convergence_of_Fourier_series ) and this probably should tell me everything I need to know, if i only were fluent in the language of convergence. I don't really know the significance of the different types of convergence (uniform, pointwise etc.) and since I'm a physicist I suspect that this might not be of very much importance since we usually assume all functions are "nice" in physics ("nice" being the appropriate simplification in the problem at hand). I vaguely remember something about L^2 functions being important for this stuff - does this have any significance? Something to compare with is perhaps analytic functions and Taylor series - what would be the analog of analytic functions in the case of Fourier series?

So what I'm asking is: when is a function "equal to" its Fourier series? Is "equal to" the same as some form of convergence? Are there "analytic functions" for Fourier series?

What I'm interested in is if there is some simple criteria which will almost always be satisfied for problems in physics. Please be gentle with me, I have forgotten a lot of this stuff and I know I'm far from an expert. :shy: