Recurrence equations and their classical orthogonal polynomial solutions on a quadratic or a q-quadratic lattice

DOI10.1080/10236198.2019.1627346zbMath1484.65333arXiv1901.03672OpenAlexW2963653832MaRDI QIDQ5239031

Daniel D. Tcheutia

Publication date: 21 October 2019

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.03672

zbMATH Keywords

classical orthogonal polynomialsthree-term recurrence equationdivided-difference equationretode

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) Computational aspects of special functions (33F99) Numerical aspects of recurrence relations (65Q30) Numerical methods for difference equations (65Q10)

Related Items (6)

Charting the 𝑞-Askey scheme ⋮ Solution of an open problem about two families of orthogonal polynomials ⋮ Open problem in orthogonal polynomials ⋮ Bound states and the potential parameter spectrum ⋮ Orthogonal Polynomials and Computer Algebra ⋮ A unified construction of all the hypergeometric and basic hypergeometric families of orthogonal polynomial sequences

Uses Software

• Maple
• DLMF
• rec2ortho
• retode

Cites Work

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• On moments of classical orthogonal polynomials
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• Representations of orthogonal polynomials
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• Recurrence equations and their classical orthogonal polynomial solutions
• Special nonuniform lattice (snul) orthogonal polynomials on discrete dense sets of points
• Some combinatorial and analytical identities
• Connection and linearization coefficients of the Askey-Wilson polynomials
• Solution of an open problem about two families of orthogonal polynomials
• On structure formulas for Wilson polynomials
• Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy
• Multivariable Meixner, Krawtchouk, and Meixner–Pollaczek polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• On difference equations for orthogonal polynomials on nonuniform lattices¹

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