(adsbygoogle = window.adsbygoogle || []).push({}); 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?..

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Borel resummation

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**