How Can Renormalization Methods Remove Singularities in Divergent Series?

[eljose]

let be the completely divergent series at $$\epsilon\rightarrow{0}$$ in the form of:

$$\sum_{n=0}^{\infty}\frac{a(n)g^{n}}{\epsilon^{n}}$$

where g is the coupling constant of our theory..then let,s suppose this series is summable and that we can get the correct result S

$$S=S(g,\epsilon)$$ then let,s suppose that S have a singularity at
$$\epsilon=0$$ my question is how we could remove this singularity by renormalization methods...thanks.

 

[quantumdude]

I'm scooting this back out of the Homework section, because it's not an undergraduate level question, and I don't think that it is a textbook question anyway. Eljose tends to work on more open-ended stuff.