Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook