Transformation to canonical form for uniform asymptotic expansions
type: Item
instance of: scholarly article
title: Transformation to canonical form for uniform asymptotic expansions
zbMATH Open document ID: 0701.30040
DOI: 10.1016/0022-247X(90)90295-Q
author: C. K. Qu
author: Roderick Wong
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: Uniform asymptotic expansions of contour integrals are often obtained by transforming the dominant part of the integrand into a canonical form, for instance into a phase function in the form of a polynomial of low degree. The cubic polynomial is used for obtaining an asymptotic expansion in terms of Airy functions. The present paper generalizes the existing results in two directions: the phase function may have a pole in the domain of interest and a logarithmic singularity; the singularities may collide, under the influence of one or two parameters, with saddle points. The mapping behind this transformation is investigated by a process of successive iteration. This general result is quite important in the study of uniform expansions of integrals.
Mathematics Subject Classification ID: 30E15
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 4148506
zbMATH Keywords: uniform asymptotic expansion of integrals
zbMATH Keywords: transformation to canonical form
reviewed by: Nico M. Temme
MaRDI profile type: Publication
cites work: Q3251584
cites work: Uniform Asymptotic Expansions of Laguerre Polynomials
cites work: Transformation of an analytic function of several variables to a canonical form
cites work: Laplace type integrals: transformation to standard form and uniform asymptotic expansions
cites work: Q3732251
cites work: Asymptotic estimates for Laguerre polynomials
cites work: Uniform Asymptotic Expansions of a Class of Integrals in Terms of Modified Bessel Functions, with Application to Confluent Hypergeometric Functions
description: scientific article; zbMATH DE number 4148506