Regularized Casimir energy for an infinite dielectric cylinder subject to light-velocity conservation

The Casimir energy of a dilute dielectric cylinder, with the same light-velocity as in its surrounding medium, is evaluated exactly to first order in ξ2=ε1−ε2ε1+ε22 (where ε1,ε2 are the dielectric constants of the cylinder and of its environment), and numerically to higher orders in ξ2. The first part is carried out using addition formulas for Bessel functions, and no Debye expansions are required.