Differential equations for generalized Jacobi polynomials

DOI10.1016/S0377-0427(99)00338-6zbMath0970.33004arXivmath/9908162MaRDI QIDQ5928280

Roelof Koekoek, J. Koekoek

Publication date: 2000

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

Full work available at URL: https://arxiv.org/abs/math/9908162

zbMATH Keywords

differential equationsgeneralized Jacobi polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Ordinary differential equations of infinite order (34A35)

Related Items (49)

Differential operators having Sobolev-type Jacobi polynomials as eigenfunctions. ⋮ Generating functions and companion symmetric linear functionals ⋮ The higher-order differential operator for the generalized Jacobi polynomials -- new representation and symmetry ⋮ The differential equation for Jacobi-Sobolev orthogonal polynomials with two linear perturbutions ⋮ Some extremal problems for algebraic polynomials in loaded spaces ⋮ Askey-Wilson type functions with bound states ⋮ The Darboux process and a noncommutative bispectral problem: some explorations and challenges ⋮ Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions ⋮ An elementary representation of the higher-order Jacobi-type differential equation ⋮ Fourth order partial differential equations for Krall-type orthogonal polynomials on the triangle ⋮ 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 ⋮ The Stenger conjectures and the \(A\)-stability of collocation Runge-Kutta methods ⋮ Zeros of orthogonal polynomials generated by canonical perturbations of measures ⋮ Generalized little $q$-Jacobi polynomials as eigensolutions of higher-order $q$-difference operators ⋮ Bispectrality of Charlier type polynomials ⋮ Krall-Jacobi commutative algebras of partial differential operators ⋮ On potential functions associated with eigenfunctions of the discrete Sturm-Liouville operator ⋮ Orthogonality for a class of generalised Jacobi polynomial P^α,β_ν(x) ⋮ 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 ⋮ A note on the Koekoeks' differential equation for generalized Jacobi polynomials ⋮ Using \(\mathcal D\)-operators to construct orthogonal polynomials satisfying higher order \(q\)-difference equations ⋮ Constructing Krall-Hahn 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 ⋮ Orthogonal polynomial solutions of linear ordinary differential equations ⋮ A method to study the Krall and \(q\)-Krall polynomials ⋮ Self-adjoint differential equations for classical orthogonal polynomials ⋮ The algebras of difference operators associated to Krall-Charlier orthogonal polynomials ⋮ Orthogonal polynomial solutions of spectral type differential equations: Magnus' conjecture ⋮ Bivariate generalized shifted Gegenbauer orthogonal system ⋮ Christoffel transform of classical discrete measures and invariance of determinants of classical and classical discrete polynomials ⋮ Bispectral Laguerre type polynomials ⋮ Differential operators having Sobolev-type Gegenbauer polynomials as eigenfunctions ⋮ New examples of Krall-Meixner and Krall-Hahn polynomials, with applications to the construction of exceptional Meixner and Laguerre polynomials ⋮ Bispectral Jacobi type polynomials ⋮ Differential and difference operators having orthogonal polynomials with two linear perturbations as eigenfunctions ⋮ Bispectral dual Hahn polynomials with an arbitrary number of continuous parameters ⋮ Differential operators having symmetric orthogonal polynomials as eigenfunctions ⋮ Generalized shifted Chebyshev Koornwinder's type polynomials: basis transformations ⋮ Self-adjoint operators generated from non-Lagrangian symmetric differential equations having orthogonal polynomial eigenfunctions ⋮ Orthogonal polynomials on the unit ball and fourth-order partial differential equations

Cites Work

• Differential and difference operators having orthogonal polynomials with two linear perturbations as eigenfunctions
• A direct approach to Koekoek's differential equation for generalized Laguerre polynomials
• On a difference equation for generalizations of Charlier polynomials
• The special functions and their approximations. Vol. I, II
• Certain differential equations for Tchebycheff polynomials
• BOCHNER-KRALL ORTHOGONAL POLYNOMIALS
• THE KRALL POLYNOMIALS: A NEW CLASS OF ORTHOGONAL POLYNOMIALS
• Orthogonal polynomials satisfying fourth order differential equations
• On a Differential Equation for Koornwinder's Generalized Laguerre Polynomials
• Differential Equations for Symmetric Generalized Ultraspherical Polynomials
• On differential equations for Sobolev-type Laguerre polynomials
• A new result for Laguerre polynomials
• The jacobi inversion formula
• Orthogonal Polynomials With Weight Function (1 - x)^α( l + x)^β + Mδ(x + 1) + Nδ(x - 1)
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