Static electric fields in an infinite plane condensor with one or three homogeneous layers

Various expressions are derived for the Green's functions for a point charge in an infinite plane condensor comprising one or three homogeneous isolating parallel dielectric layers. In view of numerical evaluations needed for calculating space charge effects in detectors (e.g. RPC's) the merits of these (series and integral) representations are discussed. It turns out that in most cases the integral representations are more favourable after their convergence has been improved. This is done by subtracting simple terms having the same asymptotic behaviour as certain too slowly converging terms and adding closed expressions resulting from the integration of the simple terms. The method is demonstrated in some detail. In addition analytic expressions for the weighting field of a strip electrode are derived which allow calculation of induced signals and crosstalk.