On the electrostatic potential due to a slab shaped and a semi-infinite NaCl-type lattice

Consider N layers of a NaCl-type ionic lattice such that in every layer one has an infinite square lattice of positive and negative unit point charges. We present formulae in which the electrostatic potential in an arbitrary field point is expressed as a sum of two rapidly converging lattice sums. For N→∞ we obtain formulae applicable for a semi-infinite lattice