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Poisson sum formula

  1. Aug 25, 2006 #1
    If we have (Poisson sum formula) in the form:

    [tex] \sum_{n=-\infty}^{\infty}f(n)= \int_{-\infty}^{\infty}dx f(x) \omega (x) [/tex]

    with [tex] \omega (x) = \sum_{n=-\infty}^{\infty}e^{2i \pi nx} [/tex]

    Then my question is if we would have that:

    [tex] \sum_{n=-\infty}^{\infty} \frac{ f(n)}{ \omega (n)} = \int_{-\infty}^{\infty} dx f(x) [/tex] ??
  2. jcsd
  3. Aug 25, 2006 #2


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    You should stop and ask if:

    [tex] \omega (x) = \sum_{n=-\infty}^{\infty}e^{2i \pi nx} [/tex]

    makes any sense at all. You have an infinite sum and the terms aren't tending to zero.
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