Liouville-Green approximations for a class of linear oscillatory difference equations of the second order

DOI10.1016/0377-0427(92)90241-OzbMath0749.39001OpenAlexW2085961785MaRDI QIDQ1812972

Marco Vianello, Renato Spigler

Publication date: 25 June 1992

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(92)90241-o

zbMATH Keywords

orthogonal polynomialsasymptotic approximationoscillatory solutionslinear difference equationsLiouville-Green approximationlinear oscillatory three-term recurrence equations

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Additive difference equations (39A10) Discrete version of topics in analysis (39A12)

Related Items (9)

Canonical forms and discrete Liouville-Green asymptotics for second-order linear difference equations ⋮ Error bounds for asymptotic solutions of second-order linear difference equations. II: The first case ⋮ Asymptotic analysis of generalized Hermite polynomials ⋮ A switch convergence for a small perturbation of a linear recurrence equation ⋮ Asymptotic approximations for second-order linear difference equations in Banach algebras. II ⋮ Convergent and asymptotic methods for second-order difference equations with a large parameter ⋮ Asyptotics for linear difference equations I:basic theory ⋮ Monotone Jacobi parameters and non-Szegő weights ⋮ Liouville-Green-Olver approximations for complex difference equations

Cites Work

• Resurrecting the asymptotics of linear recurrences
• Sturmian comparison theorems for three-term recurrence equations
• Liouville-Green approximations via the Riccati transformation
• Theory of difference equations: Numerical methods and applications
• Analytic theory of singular difference equations
• Asymptotics for Solutions of Smooth Recurrence Equations
• Growth and Oscillation Properties of Second Order Linear Difference Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Liouville-Green approximations for a class of linear oscillatory difference equations of the second order