On linearization and connection coefficients for generalized Hermite polynomials

DOI10.1016/J.CAM.2011.03.010zbMath1231.33010OpenAlexW2065508374MaRDI QIDQ645685

Hamza Chaggara, Wolfram Koepf

Publication date: 10 November 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2011.03.010

zbMATH Keywords

generalized Hermite polynomialslinearization coefficientsconnection coefficientsmultiple summationmultsum package

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Computation of special functions and constants, construction of tables (65D20)

Related Items (12)

New formulas for the linearization coefficients of some nonsymmetric Jacobi polynomials ⋮ Some recurrence formulas for the Hermite polynomials and their squares ⋮ Connection coefficients for orthogonal polynomials: Symbolic computations, verifications and demonstrations in the Mathematica language ⋮ Positivity and recursion formula of the linearization coefficients of Bessel polynomials ⋮ Recurrence relations for the connection coefficients of classical orthogonal polynomials ⋮ Connection formulae between generalized Lucas polynomials and some Jacobi polynomials: application to certain types of fourth-order BVPs ⋮ A study of numerical integration based on Legendre polynomial and RLS algorithm ⋮ Exact and simple formulas for the linearization coefficients of products of orthogonal polynomials and physical application ⋮ Two-dimensional contiguous relations for the linearization coefficients of classical orthogonal polynomials ⋮ On connection coefficients of some perturbed of arbitrary order of the Chebyshev polynomials of second kind ⋮ Hermite polynomials and their applications associated with Bernoulli and Euler numbers ⋮ New product and linearization formulae of Jacobi polynomials of certain parameters

Uses Software

• Maple

Cites Work

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• Finite singularities and hypergeometric solutions of linear recurrence equations
• Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable on the lattice \(x(s)=q^{2s}\)
• Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Discrete case
• Representations of orthogonal polynomials
• Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials
• Some results on quasi-monomiality.
• Connection problems via lowering operators
• Recurrence relations for connection coefficients between two families of orthogonal polynomials
• Second-order recurrence relation for the linearization coefficients of the classical orthogonal polynomials
• Linearization coefficients for Boas-Buck polynomial sets
• Connection coefficients between Boas--Buck polynomial sets
• Generalized linearization problems
• Orthogonal Polynomials and a Discrete Boundary Value Problem I
• Linearization of the Product of Associated Legendre Polynomials
• Characterizations of generalized Hermite and sieved ultraspherical polynomials
• Dunkl–Appelld-orthogonal polynomials
• Nonnegative Expansions of Polynomials
• Tables of Zeros and Gaussian Weights of Certain Associated Laguerre Polynomials and the Related Generalized Hermite Polynomials
• A Note on the Polynomials of Hermite and Laguerre
• Generating Functions for Bessel and Related Polynomials
• Connection coefficients and zeros of orthogonal polynomials

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