Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials.

DOI10.1016/j.cam.2003.04.005zbMath1052.33006OpenAlexW2044544108MaRDI QIDQ1421234

Wolfram Koepf, André Ronveaux, Mama Foupouagnigni

Publication date: 26 January 2004

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

Full work available at URL: https://doi.org/10.1016/j.cam.2003.04.005

zbMATH Keywords

classical orthogonal polynomialsfourth-order differential equationssemi-classical orthogonal polynomialsfunctions of the second kindLaguerre-Hahn classperturbed classical orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Other special orthogonal polynomials and functions (33C47)

Related Items (12)

Factoring linear partial differential operators in \(n\) variables ⋮ On Fourth-order Difference Equations for Orthogonal Polynomials of a Discrete Variable: Derivation, Factorization and Solutions ⋮ Factorization of ℤ$$ \mathbb {Z}$$-Homogeneous Polynomials in the First q-Weyl Algebra ⋮ 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 ⋮ Fast associated classical orthogonal polynomial transforms ⋮ On co-polynomials and \(d\)-orthogonality ⋮ A general method for deriving some semi-classical properties of perturbed second degree forms: the case of the Chebyshev form of second kind ⋮ Factorization of self-adjoint ordinary differential equations ⋮ Decomposition of perturbed Chebyshev polynomials ⋮ On difference equations for orthogonal polynomials on nonuniform lattices¹ ⋮ Characterization theorem for classical orthogonal polynomials on non-uniform lattices: the functional approach

Uses Software

• gfun
• Maple
• Mathematica

Cites Work

• On orthogonal polynomials with perturbed recurrence relations
• Theory of recursive generation of systems of orthogonal polynomials: An illustrative example
• The weight functions, generating functions and miscellaneous properties of the sequences of orthogonal polynomials of the second kind associated with the Jacobi and the Gegenbauer polynomials
• Prolégomènes à l'étude des polynômes orthogonaux semi- classiques. (Preliminary remarks for the study of semi-classical orthogonal polynomials)
• Co-recursive orthogonal polynomials and fourth-order differential equation
• Fourth-order differential equation for the co-modified of semi-classical orthogonal polynomials
• Perturbations of Laguerre-Hahn linear functionals
• On semi-classical linear functionals of class \(s=1\). Classification and integral representations
• Fourth-order differential equation satisfied by the associated of any order of all classical orthogonal polynomials. A study of their distribution of zeros
• Representations of orthogonal polynomials
• Fourth-order differential equations satisfied by the generalized co- recursive of all classical orthogonal polynomials. A study of their distribution of zeros
• Results on the associated classical orthogonal polynomials
• On Co-Recursive Orthogonal Polynomials
• Associated Laguerre and Hermite polynomials
• Explicit Formulas for the Associated Jacobi Polynomials and Some Applications
• Fourth-order differential equations for numerator polynomials
• The Associated Ultraspherical Polynomials and their _q-Analogues
• Some Results on Co-Recursive Associated Laguerre and Jacobi Polynomials
• GFUN
• On Fourth-order Difference Equations for Orthogonal Polynomials of a Discrete Variable: Derivation, Factorization and Solutions
• Unnamed Item
• Unnamed Item
• 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: Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials.