Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials

DOI10.1023/A:1019139731216zbMath1047.33009OpenAlexW105368417MaRDI QIDQ1978036

A. Zarzo, Stanisław Lewanowicz, André Ronveaux, Eduardo Paciência Godoy, IvÁn Area

Publication date: 7 June 2000

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1019139731216

zbMATH Keywords

recurrence relations Fourier coefficients linearization problem connection problem q-difference equations \(q\)-classical orthogonal polynomials \(q\)-Hahn class

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) Difference equations, scaling ((q)-differences) (39A13) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (8)

Difference equations for the co-recursive \(r\)th associated orthogonal polynomials of the \(D _{q}\)-Laguerre-Hahn class. ⋮ Construction of recurrences for the coefficients of expansions in \(q\)-classical orthogonal polynomials ⋮ Basic Fourier series on a \(q\)-linear grid: convergence theorems ⋮ Formulae relating littleq-Jacobi,q-Hahn andq-Bernstein polynomials: application toq-Bézier curve evaluation ⋮ Spectral solutions for differential and integral equations with varying coefficients using classical orthogonal polynomials ⋮ Algorithmic approach for formal Fourier series ⋮ Recursion formulae for basic hypergeometric functions ⋮ Representations for the first associated \(q\)-classical orthogonal polynomials

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