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We compute the vacuum energy of a massless scalar eld obeying a Robin boundary condition ( @ @x' = ') on one plate and the Dirichlet boundary condition (' = 0) on a parallel plate. The Casimir energy density for general dimension is obtained as a function of a (the plate separation) and by studying the cylinder kernel (alias an exponential ultraviolet cuto); we construct an innite-series solution as a sum over classical paths and observe that the method of construction has broader applications. The total Casimir energy is nite after subtraction of divergences associated with the individual plates, which do not aect the force between the plates. The series for the total energy is an alternative to the integral formula of Romeo and Saharian, with which it agrees numerically.

Casimir energy with a Robin boundary: the multiple-reflection cylinder-kernel expansion