Test of Convergence

Given constant a and b, where b > 2a + 1 >0.

Under what condition that the multiple integral of:

(x^2 + y^2)^a
--------------------- dxdy is convergent.
1 + (x^2 + y^2)^b

where the integral area is the whole xy plane, which is:

R2 = {(x,y)| -inf < x < inf, -inf < y < inf }

.

Quantcast