Solving connection and linearization problems within the Askey scheme and its \(q\)-analogue via inversion formulas

DOI10.1016/S0377-0427(00)00640-3zbMath0988.33008MaRDI QIDQ5946589

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

Publication date: 20 June 2002

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

zbMATH Keywords

linearization coefficientsconnection coefficients

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 (31)

Coefficients of multiplication formulas for classical orthogonal polynomials ⋮ New formulas for the linearization coefficients of some nonsymmetric Jacobi polynomials ⋮ Zeros of quasi-orthogonal Jacobi polynomials ⋮ Connection and inversion coefficients for basic hypergeometric polynomials ⋮ Unnamed Item ⋮ Linearization coefficients for Boas-Buck polynomial sets ⋮ Linearization coefficients for Sheffer polynomial sets via lowering operators ⋮ Some new \(q\)-series identities through an extended Bailey transform ⋮ Connection formulae between generalized Lucas polynomials and some Jacobi polynomials: application to certain types of fourth-order BVPs ⋮ 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 ⋮ Certain classes of polynomial expansions and multiplication formulas. ⋮ Representations of \(q\)-orthogonal polynomials ⋮ Volterra-type convolution of classical polynomials ⋮ Classical discrete orthogonal polynomials, Lah numbers, and involutory matrices ⋮ On moments of classical orthogonal polynomials ⋮ Inversion, Multiplication and Connection Formulae of Classical Continuous Orthogonal Polynomials ⋮ Nonnegative linearization coefficients of the generalized Bessel polynomials ⋮ Linearization and Krein-like functionals of hypergeometric orthogonal polynomials ⋮ New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials ⋮ Connection coefficients between orthogonal polynomials and the canonical sequence: An approach based on symbolic computation ⋮ Approximate Calculation of Sums II: Gaussian Type Quadrature ⋮ Connection coefficients between Boas--Buck polynomial sets ⋮ Connection problems via lowering operators ⋮ Quasi-orthogonality of some hypergeometric polynomials ⋮ A general theorem on inversion problems for polynomial sets ⋮ Policy gradient in Lipschitz Markov decision processes ⋮ ON EXISTENCE OF SOLUTIONS FOR NONLINEAR Q-DIFFERENCE EQUATIONS WITH NONLOCAL Q-INTEGRAL BOUNDARY CONDITIONS ⋮ Bivariate Krawtchouk polynomials: inversion and connection problems with the NAVIMA algorithm ⋮ New product and linearization formulae of Jacobi polynomials of certain parameters ⋮ Bounds for the zeros of symmetric Kravchuk polynomials

Cites Work

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