Differential and difference operators having orthogonal polynomials with two linear perturbations as eigenfunctions

DOI10.1016/S0377-0427(98)00010-7zbMath0928.34060MaRDI QIDQ1298501

H. Bavinck

Publication date: 5 October 1999

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

zbMATH Keywords

orthogonal polynomialsinfinite order

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Difference operators (39A70) Ordinary differential equations of infinite order (34A35) Linear difference operators (47B39)

Related Items (13)

The relaxation modulus-based matrix splitting iteration method for solving a class of nonlinear complementarity problems ⋮ Differential operators having Sobolev-type Jacobi polynomials as eigenfunctions. ⋮ The differential equation for Jacobi-Sobolev orthogonal polynomials with two linear perturbutions ⋮ A note on the Koekoeks' differential equation for generalized Jacobi polynomials ⋮ Differential operator for discrete Gegenbauer-Sobolev orthogonal polynomials: eigenvalues and asymptotics ⋮ Differential equations for generalized Jacobi polynomials ⋮ Orthogonal polynomial solutions of linear ordinary differential equations ⋮ Differential operators having Sobolev-type Laguerre polynomials as eigenfunctions: New developments ⋮ Orthogonal polynomial solutions of spectral type differential equations: Magnus' conjecture ⋮ New representations of the Laguerre-Sobolev and Jacobi-Sobolev orthogonal polynomials ⋮ Differential operators having Sobolev-type Gegenbauer polynomials as eigenfunctions ⋮ Classical Sobolev orthogonal polynomials: eigenvalue problem ⋮ Differential operators having symmetric orthogonal polynomials as eigenfunctions

Cites Work

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• Differential equations of infinite order for Sobolev-type orthogonal polynomials
• The search for differential equations for certain sets of orthogonal polynomials
• Difference operators with Sobolev type Meixner polynomials as eigenfunctions
• On Orthogonal Polynomials of Sobolev Type: Algebraic Properties and Zeros
• Differential Equations for Symmetric Generalized Ultraspherical Polynomials
• Differential operators having Sobolev type Laguerre polynomials as eigenfunctions
• On differential equations for Sobolev-type Laguerre polynomials
• Orthogonal Polynomials With Weight Function (1 - x)^α( l + x)^β + Mδ(x + 1) + Nδ(x - 1)
• On polynomials orthogonal with respect to an inner product involving differences (the general case)
• Differential equations for generalized Jacobi polynomials

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