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

  1. Nov 10, 2012 #1
    can we simply truncate a Fourier series if it is divergent??

    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. jcsd
  3. Nov 11, 2012 #2

    mathman

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    Re: can we simply truncate a Fourier series if it is divergent??

    You can always truncate the series to get a finite result. However the result as a function of N does not converge to anything.
     
  4. Nov 11, 2012 #3

    AlephZero

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    Re: can we simply truncate a Fourier series if it is divergent??

    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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