- #1
zetafunction
- 391
- 0
how can we treat overlapping divergences ? i mean integrals like
[tex] \int_{0}^{\infty} dx \int_{0}^{\infty}dy \frac{1+xy}{x+y+xy+1} [/tex]
my idea is that in this case you can use polar coordinates [tex] x=rcos(u) [/tex] [tex] y=rsin(u) [/tex] , and then if you integrate over the angular variable 'u' then you have a normal divergence [tex] \int_{0}^{\infty} rf(r)dr [/tex] so there is no more overlapping.. but can this be done or you must perform a BHPZ taylor substraction ??
[tex] \int_{0}^{\infty} dx \int_{0}^{\infty}dy \frac{1+xy}{x+y+xy+1} [/tex]
my idea is that in this case you can use polar coordinates [tex] x=rcos(u) [/tex] [tex] y=rsin(u) [/tex] , and then if you integrate over the angular variable 'u' then you have a normal divergence [tex] \int_{0}^{\infty} rf(r)dr [/tex] so there is no more overlapping.. but can this be done or you must perform a BHPZ taylor substraction ??