Schloemilch series that arise in diffraction theory and their efficient computation

We are concerned with a certain class of Schloemilch series that arise naturally in the study of diffraction problems when the scatterer is a semi-infinite 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. Many of the technical details of the derivations are omitted; they can, however, be obtained from Linton 2005 Schloemilch series that arise in diffraction theory and their efficient computation Technical Report Loughborough University available online at http://www-staff.lboro.ac.uk/~macml1/schlomilch-techreport.pdf