Understanding minimal substractio for several variables

[zetafunction]

for one dimensional integral $$\int_{0}^{\infty}dxf(x)$$ i know how to make minimal substraction however for an integral in several variables how is it done ??

for example for a triple integral

$$\int_{0}^{\infty} \int_{0}^{\infty} \int_{0}^{\infty}dx dy dz f(x,y,z)$$

i must perfrom

a minimal substraction in 'x'

a minimal substraction in 'y'

a minimal substraction in 'z'

i know how to make this however what is the following step ?

a minimal substraction in 'x,y'

a minimal substraction in x,z

a minimal substraction in y,z

a minimal substraction in x,y,z

this is the part i do not know how to do

 

[mathman]

What is "minimal substraction"?

 

[zetafunction]

What is "minimal substraction"?

minimal substraction is that given a divergent integral we must substract some terms to make it convergent.

for the case of 1 dimension is very VERY easy , the problem is when you have more than one dimension

 

[mathman]

One way would be to convert to spherical coordinates. Then the problem would be one-dimensional, since ∞ appears only for the r integral.