1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Borel resummation

  1. Aug 29, 2006 #1
    Borel "resummation"...

    Let be a divergent series:

    [tex] \sum _{n=0}^{\infty} a(n) [/tex] (1)

    then if you "had" that [tex] f(x)= \sum _{n=0}^{\infty} \frac{a(n)}{n!}x^{n} [/tex]

    You could obtain the "sum" of the series (1) as [tex] S= \int_{0}^{\infty}dte^{-t}f(t) [/tex] in case the integral converges...

    - Yes that's "beatiful" the problem is ..what happens if the coefficients a(n) are complicate?..then how can you obtain the sum of the series?...

    - By the way i think that Borel resummation can be applied if [tex] f(t)=O(e^{Mt}) [/tex] M>0, but what happens if f(t) grows faster than any positive exponential?.. :cry:
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Borel resummation
  1. Strange resummation (Replies: 2)