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Just a soft question:

While studying Taylor series, we often discuss a Taylor series’s radius of convergence.

However, we rarely talk about the radius of convergence of a Fourier series, and it seems like it always converges to some value(not necessarily the correct value) and never diverges.

Is this true? If so, are there any intuitive reasons behind?

Thanks in advance.

Szeto
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    There's no such thing as a "radius of convergence" for Fourier series. The reason is that Fourier series are not a local approximation. They can converge everywhere, diverge everywhere, converge at a point and diverge at another, etc... Convergence of Fourier series is, in general, much more complicated than convergence of Taylor series. – Giuseppe Negro Mar 03 '18 at 11:09
  • For Taylor's series , within the radius the convergence is uniform which makes it useful since the series can be differentitated and integrated termwise while for Fourier series the converges is not necessarily uniform. – ibnAbu Mar 03 '18 at 11:51

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