ON INCOMPLETE AIRY FUNCTIONS AND THEIR APPLICATION TO DIFFRACTION PROBLEMS

Several diffraction problems whose solutions involve incomplete Airy functions are briefly described; general and asymptotic characteristics of these functions are summarized. A uniform asymptotic representation, in which the incomplete Airy functions serve as canonical functions, is given for the class of integrals characterized by two saddle points arbitrarily positioned relative to an end point. Proceeding from an appropriate boundary‐layer expansion, the functions and their properties are applied in a detailed analysis of the fields near the point of confluence of the caustic of a converging wave and the shadow boundary resulting from the presence of an opaque obstacle. Copyright 1969 by the American Geophysical Union.