My question is why do we define $f(\xi+0)$ as $\lim\limits_{\varepsilon \rightarrow 0} f(\xi + \varepsilon^2)$ and $f(\xi-0)$ as $\lim\limits_{\varepsilon \rightarrow 0} f(\xi - \varepsilon^2)$.
Thanks.
2026-05-05 21:11:04.1778015464
Why we assign $1/2[f(\epsilon+0) + f(\epsilon-0)]$ as the value at the discontinuity point?
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It is not that we assign that value: Fourier series simply converge to that independently of our desires!