This is the second part of a two-part paper in which a systematic method is advanced for treating separation of variables problems asymptotically as the frequency becomes large. The method assumes an integral representation in which the contour of integration is the real axis. The contour is then deformed in the neighbourhood of the real axis to derive rigorous asymptotic expansions of the field. In this paper the method is applied to scattering in homogeneous media by the circular and parabolic cylinders.
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