I would actually be very interested in the calculus. I'm sure others would be interested too. Thanks for the offer.

Dear Jeff,

I've decided to work on this tomorrow. For now I'll say this. As I said above, to my knowledge this can't be done in closed form in general so I'll find the field along an axis normal the plane of the disk passing through the center. Since the solution will have the same form if the disk had a uniform charge on it then the electric field will have the same functional form as the gravitational field. The functional form of the disk is

[tex]E_z = \frac{1}{4\pi\epsilon_0}2\pi\sigma z[1/z - 1/\sqrt{R^2 + z^2}][/tex]

So when I post the one for the gravitational field expect it to have the same form.