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Resummation of divergent integrals.

  1. Jun 26, 2008 #1
    if we can obtain resummation methods for divergent series such as

    [tex] 1-1+1-1+1-1+1-1+... [/tex] or [tex] 1!-2!+3!-4!+.. [/tex]

    my question is why is there no method to deal with divergent integrals like [tex] \int_{0}^{\infty} dx x^{s-1} [/tex] or [tex] \int_{0}^{\infty} dx (x+1)^{-1} (x^{3}+x) [/tex]
  2. jcsd
  3. Jun 26, 2008 #2
    Do you mean the ramanujan sum?
  4. Jun 26, 2008 #3

    yes something similar but for integrals instead of being valid only for series .
  5. Jun 26, 2008 #4

    matt grime

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    My question is: why should there be? If you can think of a good reason, then perhaps you will find a way to do it. (Is this you again, eljose?)
  6. Jun 26, 2008 #5
    Can you recall any method of writing an integral as a sum?
  7. Jun 26, 2008 #6
    the question is that for example in QFT many integrals diverge as [tex] \int_{0}^{\infty} dk k^{n} [/tex] that would be a good reason to try finding resummed values of integrals.
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