I am looking for a reference that proves the Gibbs phenomenon in generality. In other words, for a function $f$ which has discontinuity in $x_0$, that the max error around the discontinuity when approximating this function by a fourier series is a given value (see wikipedia's description). In wikipedia, and many other places, there is a proof for a particular example (as square wave, toothsaw, ...) is there some nice proof for the general case somewhere?
2026-05-05 08:35:01.1777970101
Proof of Gibbs's phenomenon (general case)
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