1. Initial integral-Chapter Vdealswith the information on the edge-diffractedwaves that can be obtained by an asymptotic analysis of the integral IV.2(7), i.e.,
Weare going to obtain a high-frequency asymptotic representation of this integral with by using a traditional technique for a contour integral of a rapidly oscillating function (Felsen and Marcuvitz, 1973). We will deform the contour of integration to the form that allows us to obtain the asymptotic formulas by integrating over its separate particular parts. Such parts of the contour must pass through the neighborhoods of those points of the complex plane of z, which give the essential contribution in the integral, when
The asymptotic value of the integral (1) with is formed by contributions from the neighborhoods of the singular points, where the integrand loses its analytic character, and the saddle points, which are the minimax points of the modulus of the integrand. Let us consider the behavior of the integrand in the neighborhoods of the mentioned points.