Fourth order \(q\)-difference equation for the first associated of the \(q\)-classical orthogonal polynomials

DOI10.1016/S0377-0427(98)00225-8zbMath0952.33006MaRDI QIDQ1300809

Wolfram Koepf, André Ronveaux, Mama Foupouagnigni

Publication date: 11 January 2001

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

zbMATH Keywords

\(q\)-orthogonal polynomialsfourth-order \(q\)-difference equation

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Additive difference equations (39A10) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (10)

Difference equations for the co-recursive \(r\)th associated orthogonal polynomials of the \(D _{q}\)-Laguerre-Hahn class. ⋮ On Factorization and Solutions ofq-difference Equations  Satisfied by some Classes of Orthogonal Polynomials ⋮ On Factorization and Solutions ofq-difference Equations  Satisfied by some Classes of Orthogonal Polynomials ⋮ A fourth order \(q\)-difference equation for associated discrete \(q\)-orthogonal polynomials. ⋮ The fourth-order difference equation satisfied by the associated orthogonal polynomials of the Dq-Laguerre - Hahn Class ⋮ Hypergeometric type \(q\)-difference equations: Rodrigues type representation for the second kind solution ⋮ Fourth-order difference equation satisfied by the co-recursive of \(q\)-classical orthogonal polynomials ⋮ Extensions of some results of P. Humbert on Bezout's identity for classical orthogonal polynomials ⋮ On difference equations for orthogonal polynomials on nonuniform lattices¹ ⋮ Representations for the first associated \(q\)-classical orthogonal polynomials

Uses Software

• Maple

Cites Work

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• Fourth-order difference equation for the associated classical discrete orthogonal polynomials
• Difference equation for associated polynomials on a linear lattice
• Fourth-order difference equation for the first associated of classical discrete orthogonal polynomials
• Results on the associated classical orthogonal polynomials
• Upward extension of the Jacobi matrix for orthogonal polynomials
• Inversion problems in the \(q\)-Hahn tableau
• The fourth-order difference equation satisfied by the associated orthogonal polynomials of the Dq-Laguerre - Hahn Class
• Fourth-order differential equations for numerator polynomials
• The theory of difference analogues of special functions of hypergeometric type
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen

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