Both a power series and a Fourier series can be used to approximate a function.
How do you use these differently?
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Related: Similar uses of Taylor Series and Fourier Series *AND* Connection between Fourier transform and Taylor series *AND* Is Fourier series an “inverse” of Taylor series? *AND* On the vector spaces of Taylor Series and Fourier Series. – Dave L. Renfro Nov 18 '18 at 10:05
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The proposed duplicate target emphasizes connections between a power series and a Fourier series representation, while the present Question (terse as it is) asks about how we "use these differently". I'm going to withhold voting to close until the OP has a chance to weigh in on this aspect. – hardmath Nov 18 '18 at 15:13