On generating symmetric orthogonal polynomials

DOI10.1080/17476933.2012.674522zbMath1320.33018OpenAlexW1963563243MaRDI QIDQ2855451

Wolfram Koepf, Mohammad Masjed-Jamei

Publication date: 25 October 2013

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2012.674522

zbMATH Keywords

Hankel determinantthree-term recurrence relationFavard's theoremsymmetric orthogonal polynomialssymmetric weight function

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)

Cites Work

• A basic class of symmetric orthogonal polynomials using the extended Sturm-Liouville theorem for symmetric functions
• A basic class of symmetric orthogonal functions with six free parameters
• A formula for the coefficients of orthogonal polynomials from the three-term recurrence relations
• Two classes of special functions using Fourier transforms of generalized ultraspherical and generalized Hermite polynomials

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