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Can we simply truncate a Fourier series if it is divergent?

by zetafunction
Tags: divergent, fourier, series, simply, truncate
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Nov10-12, 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.
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Nov11-12, 02:45 PM
Sci Advisor
P: 6,104
You can always truncate the series to get a finite result. However the result as a function of N does not converge to anything.
Nov11-12, 03:06 PM
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P: 7,279
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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