MHB Progress and Accomplishments: A Look at What's Been Done

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The discussion focuses on the progress and accomplishments related to Fourier Series and their convergence properties at points of discontinuity. It emphasizes that at a discontinuous point \( t_{0} \), the Fourier Series converges to the average of the left and right limits of the function. The importance of ensuring both limits exist is highlighted for proper convergence. The conversation suggests a need for verification of a solution related to this topic. Overall, the thread underscores the mathematical principles governing Fourier Series in the context of continuity and convergence.
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Uniman said:
https://www.physicsforums.com/attachments/425

It is necessary to remember that in a point $t_{0}$ where f(t) isn't continous, the Fourier Series converges to... $\displaystyle S_{0} = \frac{1}{2}\ \{\lim_{t \rightarrow t_{0} +} f(t) + \lim_{t \rightarrow t_{0} -} f(t) \}$ ... under the assumption that both limits exist...

Kind regards

$\chi$ $\sigma$
 

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