# Understanding Borel transform (sum) in QM

1. Oct 25, 2006

Hello, i have heard tat you can use Borel transform in QM so the divergent perturbation series become convergent.. i am a bit confused since if you must compute the Borel transform:

$$B(x)=\sum_{n=0}^{\infty}\frac{a(n)x^{n}}{n!}$$

But this can only be made for a few cases $$a(n)=(-1)^{n}$$ and
$$a(n)=(-1)^{n} n!$$

But if the a(n) don't follow a known pattern Borel Transform is useless..:grumpy: :grumpy:

2. Oct 25, 2006

$$\sum_{n=0}^{\infty}(a(n) x^{n})/n!$$
-the second: $$a(n)= (-1)^{n} n!$$
- And the third $$a(n)= (-1)^{n}$$