Uniform asymptotic approximation of Mathieu functions
type: Item
instance of: scholarly article
title: Uniform asymptotic approximation of Mathieu functions
zbMATH Open document ID: 0835.33014
author: T. M. Dunster
published in: Methods and Applications of Analysis
publication date: 1996-04-08T00:00:00Z
review text: Uniform asymptotic approximations are derived for solutions of Mathieu's equation \(w'' = \{2q \cos (2z) - a\} w\) for \(z\) complex, and \(q\) and \(a\) real, \(q \to \infty\). The approximations are uniformly valid for \(- 2q \leq a \leq (2 - d)q\), where \(d\) is an arbitrarily small positive constant. The approximations involve both elementary functions and Whittaker functions. Error bounds are included or available for all approximations. The paper also gives an introduction to well-known basic properties of Mathieu's equation and its solutions, which are relevant to the paper.
Mathematics Subject Classification ID: 33E10
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 34E20
zbMATH DE Number: 818489
zbMATH Keywords: Mathieu functions
zbMATH Keywords: turning point theory
zbMATH Keywords: asymptotic approximations
zbMATH Keywords: Mathieu's equation
reviewed by: Nico M. Temme
MaRDI profile type: Publication
full work available at URL: maa.1994.v1.n2.a2
OpenAlex ID: W13073111
DOI: 10.4310/MAA.1994.V1.N2.A2
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description: scientific article; zbMATH DE number 818489