Asymptotic Behavior of Integrals

Abstract

An account is given of some developments in the asymptotic evaluation of integrals of a single variable. After a discussion of Laplace integrals and quadrature formulas, estimates are provided of the errors in Laplace-type integrals and the method of steepest descents. Then Fourier transforms and the method of stationary phase are considered; integrands which are generalized functions are included and there is also a brief description of integrals of convolution type. Finally, uniformly valid formulas for the coalescence of two saddle points or of a saddle point and singularity are derived.