On a class of complete and incomplete generalized Airy functions and their application to high-frequency scattering and diffraction problems

Abstract

The generalized Airy functions and their derivations serve as canonical functions for the uniform asymptotic evaluation of a class of integrals characterized by multiple saddle points that are arbitrarily close to one another or to an integration endpoint. The complete asymptotic representations for this class of functions are rigorously derived, and some scattering and diffraction problems in which they apply are discussed.<>