WKB (Liouville-Green) analysis of second order difference equations and applications
type: Item
instance of: scholarly article
title: WKB (Liouville-Green) analysis of second order difference equations and applications
zbMATH Open document ID: 0764.41030
DOI: 10.1016/0021-9045(92)90003-7
author: Dale T. Smith
author: Jeffrey S. Geronimo
published in: Journal of Approximation Theory
publication date: 1993-01-16T00:00:00Z
review text: A discrete analog is given of the WKB or Liouville-Green approximation for the solutions of second order difference equations of the type \(d(n+1)y(n+1)-q(n)y(n)+y(n-1)=0,\) where \(d(n)\) and \(q(n)\) are sequences of complex numbers with \(d(n) \neq0,\;n=0,1,2,\ldots\). The methods are used to obtain asymptotics for polynomials orthogonal on an infinite interval whose recurrence coefficients are regularly or slowly varying.
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 89633
zbMATH Keywords: Liouville-Green approximation
reviewed by: Nico M. Temme
MaRDI profile type: Publication
full work available at URL: 0021-9045(92)90003-7
OpenAlex ID: W2087930911
cites work: Q4726487
cites work: A unified theory of regularly varying sequences
cites work: Relative asymptotics for orthogonal polynomials with unbounded recurrence coefficients
cites work: Strong asymptotics for orthogonal polynomials with regularly and slowly varying recurrence coefficients
cites work: Q5788558
cites work: A survey of general orthogonal polynomials for weights on finite and infinite intervals
cites work: Q3994847
cites work: A proof of Freud's conjecture for exponential weights
cites work: Strong asymptotics for extremal polynomials associated with weights on \({\mathbb{R}}\)
cites work: Asymptotics for orthogonal polynomials defined by a recurrence relation
cites work: On Asymptotic Average Properties of Zeros of Orthogonal Polynomials
cites work: Asymptotics for Orthogonal Polynomials Associated with $\exp ( - x^4 )$
cites work: Géza Freud, orthogonal polynomials and Christoffel functions. A case study
cites work: Q4059363
cites work: ON ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON THE REAL AXIS
cites work: Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice
cites work: Asymptotic properties of orthogonal polynomials from their recurrence formula. II
cites work: Asymptotics for orthogonal polynomials with regularly varying recurrence coefficients
cites work: Q3209604
cites work: Asymptotics for orthogonal polynomials on and off the essential spectrum
cites work: A Note on the WKB Method for Difference Equations
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description: scientific article; zbMATH DE number 89633