On Fourth-order Difference Equations for Orthogonal Polynomials of a Discrete Variable: Derivation, Factorization and Solutions

DOI10.1080/1023619031000097035zbMath1062.33010OpenAlexW1987902562MaRDI QIDQ4812831

Wolfram Koepf, André Ronveaux, Mama Foupouagnigni

Publication date: 23 August 2004

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/1023619031000097035

zbMATH Keywords

fourth-order difference equations\(\Delta\)-Laguerre-Hahn classdiscrete classical and semi-classical orthogonal polynomialsperturbed discrete orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Polynomials, factorization in commutative rings (13P05)

Related Items (7)

On Factorization and Solutions ofq-difference Equations  Satisfied by some Classes of Orthogonal Polynomials ⋮ On Factorization and Solutions ofq-difference Equations  Satisfied by some Classes of Orthogonal Polynomials ⋮ On co-polynomials and \(d\)-orthogonality ⋮ Spectral transformation associated with a perturbed \(R_I\) type recurrence relation ⋮ Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials. ⋮ On difference equations for orthogonal polynomials on nonuniform lattices¹ ⋮ Mehler-Heine type formulas for Charlier and Meixner polynomials

Uses Software

• gfun
• Maple

Cites Work

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• On orthogonal polynomials with perturbed recurrence relations
• Discrete semi-classical orthogonal polynomials: generalized Meixner
• Prolégomènes à l'étude des polynômes orthogonaux semi- classiques. (Preliminary remarks for the study of semi-classical orthogonal polynomials)
• Fourth-order differential equation for the co-modified of semi-classical orthogonal polynomials
• Fourth-order difference equation for the associated classical discrete orthogonal polynomials
• Some results on co-recursive associated Meixner and Charlier polynomials
• Perturbations of Laguerre-Hahn linear functionals
• Fourth-order differential equation satisfied by the associated of any order of all classical orthogonal polynomials. A study of their distribution of zeros
• Difference equation for associated polynomials on a linear lattice
• Fourth-order difference equation for the first associated of classical discrete orthogonal polynomials
• Representations of orthogonal polynomials
• Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials.
• Fourth-order difference equation for the associated Meixner and Charlier polynomials
• Upward extension of the Jacobi matrix for orthogonal polynomials
• The fourth-order difference equation satisfied by the associated orthogonal polynomials of the \(\Delta\)-Laguerre-Hahn class
• Characterization of the D w -Laguerre-Hahn Functionals
• On Co-Recursive Orthogonal Polynomials
• Discrete semi-classical orthogonal polynominals

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