Hi, i am stuck at this problem , let be the divergent quantity(adsbygoogle = window.adsbygoogle || []).push({});

[tex] m= clog(\epsilon) +a_{0}+a_{1}g\epsilon ^{-1}+a_{2}g\epsilon ^{-2} +a_{3}g\epsilon ^{-3}+.........+ [/tex]

where epsilon tends to 0 and g is just some coupling constant and c ,a_n are real numbers.

then i use the Borel transform of the function [tex] F(t)= \sum_{n=0}^{\infty}a_{n} \frac{t^{n}}{n!} [/tex] in this case

[tex] m= clog(\epsilon)+ \int_{0}^{\infty}dtF(t/\epsilon)e^{-t} [/tex]

my question is, does this last expression have only 2 divergent quantities ? , mainly the one due to log(e) and the second involving the poles of [tex] F(t/\epsilon) [/tex]

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

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!

# Perturbation theory.

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

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