Classes of bivariate orthogonal polynomials

DOI10.3842/SIGMA.2016.021zbMath1333.33019arXiv1502.07256OpenAlexW1532702160MaRDI QIDQ254668

Ruiming Zhang, Mourad E. H. Ismail

Publication date: 8 March 2016

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.07256

zbMATH Keywords

generating functionsladder operators\(q\)-\(2D\)-Jacobi polynomials\(q\)-\(2D\)-Laguerre polynomials\(q\)-Sturm-Liouville equationsbiorthogonal functionsdisc polynomialsRodrigues fomulasZernike polynomials

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) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50) Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable (33D50)

Related Items (12)

Multivariate holomorphic Hermite polynomials ⋮ A review of multivariate orthogonal polynomials ⋮ Interbasis expansions in the Zernike system ⋮ Quantum superintegrable Zernike system ⋮ Superintegrable classical Zernike system ⋮ Modified 2D-complex Hermite polynomials: their quasi-monomiality and operational identities ⋮ Combinatorial and analytic properties of the \(n\)-dimensional Hermite polynomials ⋮ A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials ⋮ Spherical geometry, Zernike’s separability, and interbasis expansion coefficients ⋮ Nonlinear coherent states associated with a measure on the positive real half line ⋮ Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics ⋮ Lie-type operational approach to modified 2D-Laguerre polynomials

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