What could I say when asked to "comment on the accuracy of Fourier series at discontinuities"? It is very vague, though I reckon it alludes to the W-G phenomenon. I have read the wiki page on Gibbs phenomenon, but I don't know what to say about the accuracy. Thanks in advance!
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HINT: Consider step function $f(x)$ which is $1$ for $x > 0$ and zero for $x<0$ and equal to some value $a$ at $x=0$, find its Fourier series, and compare its value to the value of the function at the discontinuity, does it depend on $a$ ?