Representations of \(q\)-orthogonal polynomials

DOI10.1016/j.jsc.2012.03.002zbMath1247.33015OpenAlexW36283327MaRDI QIDQ438688

Mama Foupouagnigni, Wolfram Koepf, P. Njionou Sadjang, Daniel D. Tcheutia

Publication date: 31 July 2012

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2012.03.002

zbMATH Keywords

linearization coefficientsconnection coefficients\(q\)-hypergeometric representationinversion coefficientsorthogonal polynomials of \(q\)-hahn tableaustructure formulas

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Generalized hypergeometric series, ({}_pF_q) (33C20) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (10)

Coefficients of multiplication formulas for classical orthogonal polynomials ⋮ Connection and inversion coefficients for basic hypergeometric polynomials ⋮ Quasi-orthogonality of some hypergeometric and \(q\)-hypergeometric polynomials ⋮ Recurrence relations for the connection coefficients of classical orthogonal polynomials ⋮ The power collection method for connection relations: Meixner polynomials ⋮ On moments of classical orthogonal polynomials ⋮ Classical Orthogonal Polynomials of a Discrete and a q-Discrete Variable ⋮ Orthogonal Polynomials and Computer Algebra ⋮ A general theorem on inversion problems for polynomial sets ⋮ Dual and triple equations andq-orthogonal polynomials

Uses Software

• SumTools
• retode

Cites Work

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• Algorithmic determination of \(q\)-power series for \(q\)-holonomic functions
• Hypergeometric solutions of linear recurrences with polynomial coefficients
• Transverse limits in the Askey tableau
• \(q\)-hypergeometric solutions of \(q\)-difference equations
• Representations of orthogonal polynomials
• Construction of recurrences for the coefficients of expansions in \(q\)-classical orthogonal polynomials
• Extensions of some results of P. Humbert on Bezout's identity for classical orthogonal polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
• Solving connection and linearization problems within the Askey scheme and its \(q\)-analogue via inversion formulas
• On a structure formula for classical \(q\)-orthogonal polynomials
• On the \(q\)-polynomials: A distributional study

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