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I believe the Ewald sum of potentials over the lattice of images
converges quite slowly with distance from the original unit cell of
the actual paper.
... I used the all purpose hedge word
"approximated." Nevertheless, the proof may be in the pudding.
Since the resulting potential visibly (almost) satisfies the
required boundary conditions, the uniqueness property
(approximately) guarantees the solution. How's that for more
hedging?