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Blanking on word for kind of convergence of a sum

  1. Sep 19, 2013 #1

    Office_Shredder

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    I have a sum
    [tex] \sum_{n=-\infty}^{\infty} f(n) [/tex]
    which I do not want to consider the convergence of in the normal sense, but I want to talk about the limit
    [tex] \lim_{N\to \infty} \sum_{n=-N}^{N} f(n). [/tex]

    I know that when this limit exists the sum is _____ convergent, or is a _____ sum, where _____ is something like principal, or first order, or perhaps a name like a Dirichlet sum (I'm making these up of course). Does anybody know what the word I am looking for is?
     
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  3. Sep 19, 2013 #2

    micromass

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    Seems like you want the (Cauchy) principal value of the series. This is a well-known thing for integrals, but I've seen the term used for series too.
     
  4. Sep 19, 2013 #3

    Office_Shredder

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    That is exactly the term I was looking for. See, I knew the word principal was involved somehow :tongue:
     
  5. Sep 21, 2013 #4
    Fourier.
     
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