  When evaluating the electrostatic potential, periodic boundary conditions in
one, two or three of the spatial dimensions are often needed for different
applications. The triply periodic Ewald summation formula is classical, and
Ewald summation formulas for the other two cases have also been derived. In
this paper, derivations of the Ewald sums in the doubly and singly periodic
cases are presented in a uniform framework based on Fourier analysis, which
also yields a natural starting point for FFT-based fast summation methods.
