Second-order recurrence relation for the linearization coefficients of the classical orthogonal polynomials

DOI10.1016/0377-0427(95)00033-XzbMath0885.33003MaRDI QIDQ1919471

Stanisław Lewanowicz

Publication date: 13 October 1996

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

zbMATH Keywords

recurrence relationclassical orthogonal polynomials

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 (18)

Linearization coefficients for Boas-Buck polynomial sets ⋮ Algorithms for construction of recurrence relations for the coefficients of the Fourier series expansions with respect to classical discrete orthogonal polynomials ⋮ Spectral Lanczos’ Tau Method for Systems of Nonlinear Integro-Differential Equations ⋮ 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 ⋮ Rényi entropies, \(L_q\) norms and linearization of powers of hypergeometric orthogonal polynomials by means of multivariate special functions ⋮ On linearization and connection coefficients for generalized Hermite polynomials ⋮ On the connection and linearization problem for discrete hypergeometric \(q\)-polynomials ⋮ Recurrence relation approach for expansion and connection coefficients in series of classical discrete orthogonal polynomials ⋮ Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable ⋮ Computing expansions coefficients for Laguerre polynomials ⋮ Approximating the solution of integro-differential problems via the spectral tau method with filtering ⋮ Recurrences and explicit formulae for the expansion and connection coefficients in series of classical discrete orthogonal polynomials ⋮ The combinatorics of a class of representation functions ⋮ Linearization and connection coefficients for hypergeometric-type polynomials ⋮ On the linearization problem involving Pochhammer symbols and their \(q\)-analogues ⋮ Recurrence relation approach for expansion and connection coefficients in series of Hahn polynomials ⋮ On the coefficients of integrated expansions of Bessel polynomials

Cites Work

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• The three-term recurrence relation and the differentiation formulas for hypergeometric-type functions
• Results on the associated classical orthogonal polynomials
• Linearization of Products of Jacobi Polynomials.
• Linearization of Arbitrary products of classical orthogonal polynomials
• Products of Laguerre Polynomials
• A Note on the Polynomials of Hermite and Laguerre

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