Resummation of divergent integrals.

[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 $$\int_{0}^{\infty} dx (x+1)^{-1} (x^{3}+x)$$

 

[Santa1]

Do you mean the ramanujan sum?

 

[mhill]

Do you mean the ramanjuan sum?

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

 

[matt grime]

my question is why is there no method to deal with divergent integrals

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?)

 

[Santa1]

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

 

[mhill]

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?)

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.