Characterization theorem for classical orthogonal polynomials on non-uniform lattices: the functional approach

DOI10.1080/10652469.2010.546996zbMath1234.33012OpenAlexW2152964321MaRDI QIDQ3107301

Maurice Kenfack-Nangho, Mama Foupouagnigni, Salifou Mboutngam

Publication date: 23 December 2011

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: http://nbn-resolving.org/urn:nbn:de:hebis:34-2010083034418

zbMATH Keywords

classical orthogonal polynomialsRiccati equationlinear functionalsnon-uniform latticesdivided-difference equationsstructure relationsfunctional approach

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (18)

On structure formulas for Wilson polynomials ⋮ A characterization of continuous \(q\)-Jacobi, Chebyshev of the first kind and Al-Salam chihara polynomials ⋮ On the modifications of semi-classical orthogonal polynomials on nonuniform lattices ⋮ On another characterization of Askey-Wilson polynomials ⋮ On the functional equation for classical orthogonal polynomials on lattices ⋮ Remarks on Askey-Wilson polynomials and Meixner polynomials of the second kind ⋮ On solutions of holonomic divided-difference equations on nonuniform lattices ⋮ On exponential and trigonometric functions on nonuniform lattices ⋮ On non-linear characterizations of classical orthogonal polynomials ⋮ Divided-difference equation, inversion, connection, multiplication and linearization formulae of the continuous Hahn and the Meixner-Pollaczek polynomials ⋮ Characterization of orthogonal polynomials on lattices ⋮ A characterization of Askey-Wilson polynomials ⋮ Discrete semi-classical orthogonal polynomials of class one on quadratic lattices ⋮ Hypergeometric Multivariate Orthogonal Polynomials ⋮ Orthogonal polynomials on systems of non-uniform lattices from compatibility conditions ⋮ On the polynomial solution of divided-difference equations of the hypergeometric type on nonuniform lattices ⋮ A characterization theorem for semi-classical orthogonal polynomials on non-uniform lattices ⋮ On the second-order holonomic equation for Sobolev-type orthogonal polynomials

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• Another Characterization of the Classical Orthogonal Polynomials
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