# Resummation of divergent integrals.

1. Jun 26, 2008

### mhill

if we can obtain resummation methods for divergent series such as

$$1-1+1-1+1-1+1-1+...$$ or $$1!-2!+3!-4!+..$$

my question is why is there no method to deal with divergent integrals like $$\int_{0}^{\infty} dx x^{s-1}$$ or $$\int_{0}^{\infty} dx (x+1)^{-1} (x^{3}+x)$$

2. Jun 26, 2008

### Santa1

Do you mean the ramanujan sum?

3. Jun 26, 2008

### mhill

yes something similar but for integrals instead of being valid only for series .

4. Jun 26, 2008

### matt grime

My question is: why should there be? If you can think of a good reason, then perhaps you will find a way to do it. (Is this you again, eljose?)

5. Jun 26, 2008

### Santa1

Can you recall any method of writing an integral as a sum?

6. Jun 26, 2008

### mhill

the question is that for example in QFT many integrals diverge as $$\int_{0}^{\infty} dk k^{n}$$ that would be a good reason to try finding resummed values of integrals.