I'm trying to numerically evaluate this integral in Matlab using quad and dblguad functions, but I'm running into problems due to the way the inner integrals are structured. I cant use dblquad (double integration) to integrate over $u$ and $v$ because the function in the innermost integral is a function of $u$, $v$ and $z$. I guess my question is there any way I can get $z$ out of the two inner integrals. This way I can evaluate the inner integrals and all is left is just a function of $z$ for the outermost integral.
This is my code, but it's not working, because of the problem I mentioned above.
F1 = @(u,v) u.*v.*exp(-0.5.*u.^2)./(1+2*z.*u.*v); F2 = @(v) v; F3 = @(z) exp(-z)./sqrt(z); I1 = dblquad(F1,0,1e5,2,1e5); I2 = quad(F2,2,1e5); quad(F3*exp(-(I2-I1)),0,1e5);