Constructing bispectral dual Hahn polynomials

DOI10.1016/j.jat.2014.09.004zbMath1306.33017arXiv1407.6973OpenAlexW2040376575MaRDI QIDQ476124

Antonio J. Duran

Publication date: 28 November 2014

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

Full work available at URL: https://arxiv.org/abs/1407.6973

zbMATH Keywords

orthogonal polynomialsKrall polynomialsdual Hahn polynomialsdifference operators and equations

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) Other functions coming from differential, difference and integral equations (33E30)

Related Items

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, Convergence rates of exceptional zeros of exceptional 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 Jacobi polynomials, Bispectrality of Meixner type polynomials, Constructing Krall-Hahn 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, Jacobi Polynomials as su(2, 2) Unitary Irreducible Representation, New examples of Krall-Meixner and Krall-Hahn polynomials, with applications to the construction of exceptional Meixner and Laguerre 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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Using \(\mathcal D\)-operators to construct orthogonal polynomials satisfying higher order difference or differential equations
• Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schrödinger Hamiltonians
• Using \(\mathcal D\)-operators to construct orthogonal polynomials satisfying higher order \(q\)-difference equations
• Differential equations in the spectral parameter
• Krall-Jacobi commutative algebras of partial differential operators
• Discrete bispectral Darboux transformations from Jacobi operators.
• Askey-Wilson type functions with bound states
• An extension of Bochner's problem: exceptional invariant subspaces
• A method of constructing Krall's polynomials
• Some functions that generalize the Krall-Laguerre polynomials
• Difference equations for generalized Meixner polynomials
• Rational spectral transformations and orthogonal polynomials
• On a difference equation for generalizations of Charlier polynomials
• Orthogonal polynomials satisfying higher-order difference equations
• Krall-Laguerre commutative algebras of ordinary differential operators
• Exceptional Meixner and Laguerre orthogonal polynomials
• Constructing bispectral orthogonal polynomials from the classical discrete families of Charlier, Meixner and Krawtchouk
• Exceptional Charlier and Hermite orthogonal polynomials
• Dual Christoffel Transformations
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations
• THE KRALL POLYNOMIALS: A NEW CLASS OF ORTHOGONAL POLYNOMIALS
• AN APPLICATION OF A NEW THEOREM ON ORTHOGONAL POLYNOMIALS AND DIFFERENTIAL EQUATIONS
• The Stieltjes Moments Problem for Rapidly Decreasing Functions
• Orthogonal Polynomials, Duality and Association Schemes
• On a Differential Equation for Koornwinder's Generalized Laguerre Polynomials
• Differential Equations for Symmetric Generalized Ultraspherical Polynomials
• Dual $-1$ Hahn polynomials: “Classical” polynomials beyond the Leonard duality
• Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
• Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials
• Differential equations for generalized Jacobi polynomials