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Can someone point me to the full derivation of the Fourier Series? I'm having problems understanding how the a's and b's coeffients are worked out.

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    This isn't really a physics question. I'll flag for the mods to migrate it to math.stackexchange.2011-02-17
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    I don't quite understand the question: the Fourier Series is a *definition*: for any integrable function on a closed interval, its coefficients are given by a particular formula: see e.g. http://en.wikipedia.org/wiki/Fourier_series#Definition. So what exactly is it that you want to work out?2011-02-23
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    I think the OP wants to see a proof that if $f(x) = \sum a_n\cos nx + b_n\sin nx$, where the convergence is (at least) pointwise, then the coefficients $a_n$ and $b_n$ are given by those standard formulas.2011-02-23

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