On asymptotics of a second order linear ODE with a turning-regular singular point
type: Item
instance of: scholarly article
title: On asymptotics of a second order linear ODE with a turning-regular singular point
zbMATH Open document ID: 1232.34122
author: Minoru Nakano
published in: Tokyo Journal of Mathematics
publication date: 2010-08-30T00:00:00Z
review text: This paper deals with the equation \[ \varepsilon^2 \frac{d^2y}{dx^2} -\Bigl(x^m- \frac{\varepsilon}{x} \Bigr) y=0 \] in a neighbourhood of the regular singular point \(x=0,\) where \(\varepsilon >0\) is a small parameter and \(m\) is a positive integer. The outer solution for \(K\varepsilon ^{1/(m+1)} \leq |x|\leq x_0\) and the inner solution for \(0<\varepsilon^{-1/(m+1)}|x| <\infty\) are given in a sector. For the inner solution a canonical domain and Stokes curves are discussed, and a matching matrix connecting the outer and inner solutions is obtained.
reviewed by: Shun Shimomura
Mathematics Subject Classification ID: 34M60
Mathematics Subject Classification ID: 34M03
Mathematics Subject Classification ID: 34M40
zbMATH DE Number: 5776104
zbMATH Keywords: asymptotics
zbMATH Keywords: turning point
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1279719583
OpenAlex ID: W2026790624
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DOI: 10.3836/TJM/1279719583
description: scientific article; zbMATH DE number 5776104