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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.