\(d\)-orthogonal analogs of classical orthogonal polynomials

DOI10.3842/SIGMA.2018.063zbMath1393.33012arXiv1609.06157MaRDI QIDQ723906

Emil Horozov

Publication date: 24 July 2018

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

Full work available at URL: https://arxiv.org/abs/1609.06157

zbMATH Keywords

generating functionsgeneralized hypergeometric functionsbispectral problemfinite recurrence relations\(d\)-orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

Related Items

Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence, Product of two hypergeometric functions with power arguments, On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials, On the orthogonality of partial sums of generalized hypergeometric series

Uses Software

• DLMF

Cites Work

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• Automorphisms of algebras and Bochner's property for vector orthogonal polynomials
• \(d\)-orthogonal polynomials and \(\mathfrak {su}(2)\)
• Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits
• Differential equations in the spectral parameter
• Vector orthogonal relations. Vector QD-algorithm
• Some families of hypergeometric polynomials and associated integral representations
• On \(d\)-symmetric classical \(d\)-orthogonal polynomials
• Two-dimensional orthogonal polynomials, their associated sets and the co- recursive sets
• Local universality in biorthogonal Laguerre ensembles
• Jensen polynomials and the Turán and Laguerre inequalities
• Generalized Hermite polynomials and supergaussian forms
• Operational formulas connected with two generalizations of Hermite polynomials
• Intersection theory on the moduli space of curves and the matrix Airy function
• An introduction to matching polynomials
• Bispectral algebras of commuting ordinary differential operators
• Multiple orthogonal polynomials
• Higher-order Fibonacci numbers
• Some discrete \(d\)-orthogonal polynomial sets.
• Biorthogonal ensembles
• General methods for constructing bispectral operators
• Muttalib-Borodin ensembles in random matrix theory -- realisations and correlation functions
• Biorthogonal polynomials suggested by the Laguerre polynomials
• Asymptotic formulae of Mehler-Heine-type for certain classical polyorthogonal polynomials
• Large \(n\) limit of Gaussian random matrices with external source. II
• The higher-order matching polynomial of a graph
• Open intersection numbers, Kontsevich-Penner model and cut-and-join operators
• Cut-and-join description of generalized Brezin-Gross-Witten model
• UNITARY MATRIX INTEGRALS IN THE FRAMEWORK OF THE GENERALIZED KONTSEVICH MODEL
• Mehler-Heine asymptotics for multiple orthogonal polynomials
• The Gould-Hopper polynomials in the Novikov-Veselov equation
• Automorphisms of the Heisenberg–Weyl algebra and d-orthogonal polynomials
• Random matrix model with external source and a constrained vector equilibrium problem
• Multiple orthogonal polynomials in random matrix theory
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Multiple orthogonal polynomials for classical weights
• A generalized hypergeometric d -orthogonal polynomial set
• Generalized analytic functions
• Hermite-Padé approximations and multiple orthogonal polynomial ensembles
• Proof of a conjecture by Gazeau et al. using the Gould-Hopper polynomials
• Generating Functions for Jacobi and Laguerre Polynomials
• Some classical multiple orthogonal polynomials
• Irrationality of infinitely many values of the zeta function at odd integers.
• Mehler-Heine type formulas for Charlier and Meixner polynomials