Resummation of divergent integrals.

  • Thread starter mhill
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  • #1
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Main Question or Discussion Point

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]
 

Answers and Replies

  • #2
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Do you mean the ramanujan sum?
 
  • #3
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Do you mean the ramanjuan sum?

yes something similar but for integrals instead of being valid only for series .
 
  • #4
matt grime
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my question is why is there no method to deal with divergent integrals

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?)
 
  • #5
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Can you recall any method of writing an integral as a sum?
 
  • #6
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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?)
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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