Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable

DOI10.1016/S0377-0427(96)00104-5zbMath0877.33003MaRDI QIDQ5961656

Stanisław Lewanowicz

Publication date: 9 November 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

recurrence relationsMeixner polynomialsKrawtchouk polynomialsconnection coefficientsCharlier polynomialsHahn polynomialsorthogonal polynomials of a discrete variable

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)

Related Items (24)

Construction of recurrences for the coefficients of expansions in \(q\)-classical orthogonal polynomials ⋮ Linearization coefficients for Boas-Buck polynomial sets ⋮ On the fourth-order difference equation for the associated Meixner polynomials ⋮ Connection coefficients for orthogonal polynomials: Symbolic computations, verifications and demonstrations in the Mathematica language ⋮ Recurrence relations for the connection coefficients of classical orthogonal polynomials ⋮ Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Discrete case ⋮ Corrigendum: Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Discrete case ⋮ Fourth-order difference equation for the first associated of classical discrete orthogonal polynomials ⋮ Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials ⋮ Divided-difference equation, inversion, connection, multiplication and linearization formulae of the continuous Hahn and the Meixner-Pollaczek polynomials ⋮ On connection coefficients of some perturbed of arbitrary order of the Chebyshev polynomials of second kind ⋮ Inversion problems in the \(q\)-Hahn tableau ⋮ The fourth-order difference equation satisfied by the associated orthogonal polynomials of the Dq-Laguerre - Hahn Class ⋮ Connection coefficients between orthogonal polynomials and the canonical sequence: An approach based on symbolic computation ⋮ On the connection and linearization problem for discrete hypergeometric \(q\)-polynomials ⋮ Solving connection and linearization problems within the Askey scheme and its \(q\)-analogue via inversion formulas ⋮ Fourth-order difference equation satisfied by the co-recursive of \(q\)-classical orthogonal polynomials ⋮ Expansion of multivariate polynomials in products of univariate orthogonal polynomials: Discrete case ⋮ Recurrence relation approach for expansion and connection coefficients in series of classical discrete orthogonal polynomials ⋮ Recurrences and explicit formulae for the expansion and connection coefficients in series of classical discrete orthogonal polynomials ⋮ Connection problems for polynomial solutions of nonhomogeneous differential and difference equations ⋮ Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable on the lattice \(x(s)=q^{2s}\) ⋮ Recurrence relation approach for expansion and connection coefficients in series of Hahn polynomials ⋮ Bivariate Krawtchouk polynomials: inversion and connection problems with the NAVIMA algorithm

Uses Software

• Maple

Cites Work

• Difference equation for associated polynomials on a linear lattice
• Projection formulas for orthogonal polynomials of a discrete variable
• Recurrence relations for connection coefficients between two families of orthogonal polynomials
• Results on the associated classical orthogonal polynomials
• Second-order recurrence relation for the linearization coefficients of the classical orthogonal polynomials
• Corrigenda
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