  In this paper we sum over the spherical modes appearing in the expression for
the Casimir energy of a conducting sphere and of a dielectric ball (assuming
the same speed of light inside and outside), before doing the frequency
integration. We derive closed integral expressions that allow the calculations
to be done to all orders, without the use of regularization procedures. The
technique of mode summation using a contour integral is critically examined.

High Energy Physics - Theory;Condensed Matter;High Energy Physics - Phenomenology;Quantum Physics