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Can we simply truncate a Fourier series if it is divergent? 
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#1
Nov1012, 04:04 PM

P: 399

given a Fourier series of the form
[tex] \sum_{n=0}^{\infty}\frac{cos(nx)}{\sqrt{n}}[/tex] can i simply truncate this series up to some number finite N so i can get finite results ?? thanks. 


#2
Nov1112, 02:45 PM

Sci Advisor
P: 6,040

You can always truncate the series to get a finite result. However the result as a function of N does not converge to anything.



#3
Nov1112, 03:06 PM

Engineering
Sci Advisor
HW Helper
Thanks
P: 6,967

Maybe a more fundamental question is "what is your series supposed to represent?" For eaxmple, the energy (measured as the function squared) is ##\sum (1/n)## which is infinite.
As mathman said, you can do anything you like mathematically with a finite number of terms, but whether the result means anything is another question. 


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