Schlömilch series that arise in diffraction theory and their efficient computation.

We are concerned with a certain class of Schlömilch series that arise naturally in the study of diffraction problems when the scatterer is a periodic structure. By combining new results derived from integral representations and the Poisson summation formula with known identities, we obtain expressions which enable the series to be computed accurately and efficiently. Most of the technical details of the derivations are omitted; they can, however, be obtained from the technical report [1] available online.