Difference equations and quantized discriminants for \(q\)-orthogonal polynomials

DOI10.1016/S0196-8858(02)00547-XzbMath1032.33012OpenAlexW1969767627MaRDI QIDQ1408268

Mourad E. H. Ismail

Publication date: 15 September 2003

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0196-8858(02)00547-x

zbMATH Keywords

\(q\)-difference equationsrecurrence relationsdiscriminants\(q\)-orthogonal polynomialsraising and lowering operatorscontinuous \(q\)-Jacobi polynomialsfunctions of the second kindlitte \(q\)-Jacobi polynomials

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (19)

Pair correlation of roots of rational functions with rational generating functions and quadratic denominators ⋮ Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy ⋮ Difference equations and discriminants for discrete orthogonal polynomials ⋮ 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 characterization of some \(q\)-orthogonal polynomials ⋮ Linear graininess time scales and ladder operators of orthogonal polynomials ⋮ The root distribution of polynomials with a three-term recurrence ⋮ Coherent states attached to the quantum disc algebra and their associated polynomials ⋮ Functions of the second kind for classical polynomials ⋮ Ladder operators for \(q\)-orthogonal polynomials ⋮ Connections between discriminants and the root distribution of polynomials with rational generating function ⋮ Discriminants of polynomials related to Chebyshev polynomials: the ``Mutt and Jeff syndrome ⋮ Around a Conjecture of K. Tran ⋮ \(q\)-discriminants and vertex operators ⋮ \(q\)-difference operators for orthogonal polynomials ⋮ Variations of Stieltjes-Wigert and \(q\)-Laguerre polynomials and their recurrence coefficients ⋮ On the recurrence coefficients of the generalized littleq-Laguerre polynomials ⋮ The electrostatic equilibrium problem for classical discrete orthogonal polynomials

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