  The method of images is used to calculate the Casimir energy in Euclidean
space with Dirichlet boundary conditions for two planar models, namely: i. the
non-relativistic Landau problem for a charged particle of mass m for which -
irrespective of the sign of the charge - the energy is negative, and ii. the
model of a real, massive, noninteracting relativistic scalar field theory in 2
+ 1 dimensions, for which the Casimir energy density is non-negative and is
expressed in terms of the Lerch transcendent xxx and the polylogarithm xxx with
0 < xxx < 1 and n = 2, 3.
