Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy

DOI10.1215/00277630-3140952zbMath1334.39024arXiv1204.2328OpenAlexW2963166891MaRDI QIDQ3458668

Nicholas S. Witte

Publication date: 21 December 2015

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.2328

zbMATH Keywords

orthogonal polynomialsAskey tableisomonodromic deformationsAskey-Wilson polynomialsdivided-difference operatorsnonuniform latticessemiclassical weights

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) General theory of difference equations (39A05) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Related Items (11)

The Padé interpolation method applied to \(q\)-Painlevé equations. II (differential grid version) ⋮ Recurrence relations for the moments of discrete semiclassical orthogonal polynomials ⋮ On the complex difference equation of hypergeometric type on non-uniform lattices ⋮ Comparative asymptotics for discrete semiclassical orthogonal polynomials ⋮ Lattice equations arising from discrete Painlevé systems: II. ${A}_{4}^{(1)}$ case ⋮ Discrete semi-classical orthogonal polynomials of class one on quadratic lattices ⋮ Orthogonal polynomials on systems of non-uniform lattices from compatibility conditions ⋮ The Padé interpolation method applied to additive difference Painlevé equations ⋮ Recurrence equations and their classical orthogonal polynomial solutions on a quadratic or a q-quadratic lattice ⋮ 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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