AN APPLICATION OF A NEW THEOREM ON ORTHOGONAL POLYNOMIALS AND DIFFERENTIAL EQUATIONS

DOI10.1080/16073606.1986.9631591zbMath0605.33010OpenAlexW2037617840MaRDI QIDQ3743615

Lance L. Littlejohn

Publication date: 1986

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/16073606.1986.9631591

zbMATH Keywords

distributionRodrigues formulaboundary value problem

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) Linear ordinary differential equations and systems (34A30)

Related Items (35)

The symmetric form of the Koekoeks' Laguerre type differential equation ⋮ On the classification of differential equations having orthogonal polynomial solutions. II ⋮ Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions ⋮ Differential equations having orthogonal polynomial solutions ⋮ Symmetrizability of differential equations having orthogonal polynomial solutions ⋮ From Krall discrete orthogonal polynomials to Krall polynomials ⋮ On difference operators for symmetric Krall-Hahn polynomials ⋮ Using \(\mathcal D\)-operators to construct orthogonal polynomials satisfying higher order difference or differential equations ⋮ Orthogonal polynomials satisfying higher-order difference equations ⋮ Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters ⋮ The algebra of difference operators associated to Meixner type polynomials ⋮ On optimal control of mean-field stochastic systems driven by Teugels martingales via derivative with respect to measures ⋮ Bispectrality of Charlier type polynomials ⋮ Bispectrality of Meixner type polynomials ⋮ Constructing bispectral dual Hahn polynomials ⋮ Using \(\mathcal D\)-operators to construct orthogonal polynomials satisfying higher order \(q\)-difference equations ⋮ Constructing Krall-Hahn orthogonal polynomials ⋮ Narain transform for spectral deformations of random matrix models ⋮ Differential operators having Sobolev type Laguerre polynomials as eigenfunctions ⋮ Constructing bispectral orthogonal polynomials from the classical discrete families of Charlier, Meixner and Krawtchouk ⋮ On the assignment of a Dirac-mass for a regular and semi-classical form ⋮ An application in stochastics of the Laguerre-type polynomials ⋮ The algebras of difference operators associated to Krall-Charlier orthogonal polynomials ⋮ Christoffel transform of classical discrete measures and invariance of determinants of classical and classical discrete polynomials ⋮ Bispectral Laguerre type polynomials ⋮ Orthogonal polynomials and higher order singular Sturm-Liouville systems ⋮ New examples of Krall-Meixner and Krall-Hahn polynomials, with applications to the construction of exceptional Meixner and Laguerre polynomials ⋮ Bispectral Jacobi type polynomials ⋮ More on Electrostatic Models for Zeros of Orthagonal Polynomials ⋮ More on Electrostatic Models for Zeros of Orthagonal Polynomials ⋮ Variations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomials ⋮ Bispectral dual Hahn polynomials with an arbitrary number of continuous parameters ⋮ Some functions that generalize the Krall-Laguerre polynomials ⋮ Differential equations for discrete Laguerre-Sobolev orthogonal polynomials ⋮ Symmetry factors for differential equations with applications to orthogonal polynomials

Cites Work

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• Die Charakterisierung der klassischen orthogonalen Polynome durch Sturm- Liouvillesche Differentialgleichungen
• On the classification of differential equations having orthogonal polynomial solutions
• Certain differential equations for Tchebycheff polynomials
• The Krall Polynomials as Solutions to a Second Order Differential Equation
• Symmetry Factors for Differential Equations
• THE KRALL POLYNOMIALS: A NEW CLASS OF ORTHOGONAL POLYNOMIALS
• Nonclassical Orthogonal Polynomials as Solutions to Second Order Differential Equations
• Orthogonal polynomials satisfying fourth order differential equations
• Distributional Weight Functions for Orthogonal Polynomials
• Orthogonal Polynomials With Weight Function (1 - x)^α( l + x)^β + Mδ(x + 1) + Nδ(x - 1)

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