Using \(\mathcal D\)-operators to construct orthogonal polynomials satisfying higher order difference or differential equations

DOI10.1016/J.JAT.2013.06.004zbMath1286.34114arXiv1302.0881OpenAlexW1606810440MaRDI QIDQ390620

Antonio J. Duran

Publication date: 8 January 2014

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.0881

zbMATH Keywords

Jacobi polynomialsLaguerre polynomialsMeixner polynomialsCharlier polynomialsHahn polynomialsdifferential and difference operatorsKrawtchuk polynomialsorthogonal and discrete orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10)

Related Items (29)

The higher-order differential operator for the generalized Jacobi polynomials -- new representation and symmetry ⋮ From Krall discrete orthogonal polynomials to Krall polynomials ⋮ On difference operators for symmetric Krall-Hahn polynomials ⋮ Invariance properties of Wronskian type determinants of classical and classical discrete orthogonal polynomials ⋮ Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters ⋮ The algebra of difference operators associated to Meixner type polynomials ⋮ Bispectrality of Charlier type polynomials ⋮ Exceptional Charlier and Hermite orthogonal polynomials ⋮ Bispectrality of Meixner type polynomials ⋮ Bispectral extensions of the Askey-Wilson polynomials ⋮ On the higher-order differential equations for the generalized Laguerre polynomials and Bessel functions ⋮ Constructing bispectral dual Hahn polynomials ⋮ Using \(\mathcal D\)-operators to construct orthogonal polynomials satisfying higher order \(q\)-difference equations ⋮ Constructing Krall-Hahn orthogonal polynomials ⋮ Symmetries for Casorati determinants of classical discrete orthogonal polynomials ⋮ Symmetric differential operators for Sobolev orthogonal polynomials of Laguerre- and Jacobi-type ⋮ Constructing bispectral orthogonal polynomials from the classical discrete families of Charlier, Meixner and Krawtchouk ⋮ Exceptional Meixner and Laguerre orthogonal polynomials ⋮ The algebras of difference operators associated to Krall-Charlier orthogonal polynomials ⋮ Exceptional Hahn and Jacobi orthogonal polynomials ⋮ Christoffel transform of classical discrete measures and invariance of determinants of classical and classical discrete polynomials ⋮ Bispectral Laguerre type polynomials ⋮ New Properties of the Zeros of Krall Polynomials ⋮ New examples of Krall-Meixner and Krall-Hahn polynomials, with applications to the construction of exceptional Meixner and Laguerre polynomials ⋮ Bispectral Jacobi type polynomials ⋮ Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials ⋮ Bispectral dual Hahn polynomials with an arbitrary number of continuous parameters ⋮ Differential equations for discrete Laguerre-Sobolev orthogonal polynomials ⋮ Multi-indexed Meixner and littleq-Jacobi (Laguerre) polynomials

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