Jump discontinuity with fourier series

yoq_bise
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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:

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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