Jump discontinuity with fourier series

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SUMMARY

The discussion centers on the proof of the statement regarding the Fourier series expansion of a function f(x) with a discontinuity at point y. Specifically, it asserts that f(y) equals the average of the left and right limits, expressed as f(y) = (1/2)(f(y+) + f(y-)). Participants mention consulting texts such as "Hassani," "Arfken," and "Diprima" without finding the necessary proof, indicating a gap in accessible resources on this topic.

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Hi all,
I couldn't find any proof of the following statement: The Fourier series expansion of f(x), which has a discontinuity at y, takes on the mean of the left and right limits
i.e. f(y)= (1/2)(f(y+)+f(y-))

is there anyone who can help me?
Thanks
 
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Have you tried looking in a book?
 
Yes I looked in Hassani, Arfken and Diprima but I couldn't find
Can anyone suggest other books or web sites?
 
Last edited:

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