  Bertaut's equivalent electric density idea (E. F. Bertaut, Journal de
Physique {\bf 39}, 1331 (1978)) is applied to the case of two dimensional
periodic continuous charge density distributions. The following derivation
differs from what was introduced by Bertaut. The presented method solves the
Poisson equation for the scheme of overlapping localized site densities with
periodic boundary conditions in the ($x,y$) plane and with the general finite
voltage boundary condition in the perpendicular $z$-direction.As usual the
long-range potential is calculated in the Fourier space. For the $K_{||}\ne 0$
case a Fourier transformation helps to calculate the solution in a three
dimensional periodic sense, while for %the $K_{||}=0$ %case the required charge
neutrality is the starting point. For both cases suitable representations of
the spherical harmonics are needed to arrive at expressions that are convenient
for numerical implementation. In this localized density scheme an explicit
relation can be derived between the finite voltage in $z$-direction and the
$z$-component of the dipole density.
