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answered Sum of squared/cubed combinations
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comment Proving a family of orthogonal functions is complete over a certain interval
The nice thing about Stone-Weierstrass is that all of the complicated functional analysis is encapsulated in the proof of the theorem, so if you're willing to take the proof on trust, you can use the results without having to do any analysis at all.
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answered Proving a family of orthogonal functions is complete over a certain interval
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