The Askey scheme as a four-manifold with corners

DOI10.1007/s11139-009-9208-7zbMath1195.33053arXiv0909.2822OpenAlexW3098071433MaRDI QIDQ969419

Koornwinder, Tom H.

Publication date: 7 May 2010

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.2822

zbMATH Keywords

manifold with cornershypergeometric orthogonal polynomialsthree-term recurrence relationsAskey schemelimit relations

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)

Related Items (11)

Charting the 𝑞-Askey scheme ⋮ An algebraic geometric classification of superintegrable systems in the Euclidean plane ⋮ Asymptotic Reductions Between the Wilson Polynomials and the Lower Level Polynomials of the Askey Scheme ⋮ Towards a full solution of the large N double-scaled SYK model ⋮ An algebraic geometric foundation for a classification of second-order superintegrable systems in arbitrary dimension ⋮ On lifting \(q\)-difference operators for a chain of basic hypergeometric polynomials ⋮ Recurrence coefficients and difference equations of classical discrete orthogonal and \(q\)-orthogonal polynomial sequences ⋮ Hypergeometric Multivariate Orthogonal Polynomials ⋮ Limit relations involving 2-orthogonal polynomials ⋮ Orthogonal Polynomials ⋮ A unified construction of all the hypergeometric and basic hypergeometric families of orthogonal polynomial sequences

Uses Software

• retode

Cites Work

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• Asymptotic approximations between the hahn-type polynomials and Hermite, Laguerre and charlier polynomials
• Limits of some q-Laguerre polynomials
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• On the limit relations between classical continuous and discrete orthogonal polynomials
• Transverse limits in the Askey tableau
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• Approximations of orthogonal polynomials in terms of Hermite polynomials
• Recurrence equations and their classical orthogonal polynomial solutions
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• Topologie de certains espaces de plongements
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• The Hahn and Meixner polynomials of an imaginary argument and some of their applications
• Continuous Hahn polynomials
• The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis

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