On orthogonal polynomials: semiclassical and of second category

DOI10.1080/10652469.2011.553612zbMath1241.33010OpenAlexW2037834205MaRDI QIDQ2880440

Atia, Mohamed Jalel, S. Leffet

Publication date: 13 April 2012

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2011.553612

zbMATH Keywords

semiclassical orthogonal polynomialsthree term recurrence relationrecurrence coefficientsLaguerre-Freud equationsPearson equationorthogonal polynomials of the second category

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 (3)

Some linear functionals having classical orthogonal polynomials as moments ⋮ A proof of a conjecture about a symmetric system of orthogonal polynomials ⋮ Cubic decomposition of a family of semiclassical polynomial sequences of class one

Uses Software

• OPQ

Cites Work

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• On a conjecture of A. Magnus concerning the asymptotic behavior of the recurrence coefficients of the generalized Jacobi polynomials
• Orthogonality with respect to the sum of two semiclassical regular linear forms
• Laguerre-Freud's equations for the recurrence coefficients of semi- classical orthogonal polynomials
• Some generalized Jacobi polynomials.
• Strong asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight.
• Semi-Classical Linear Functionals and Integral Representation
• Semi-classical linear functionals and integral representation II
• Explicit representations of some orthogonal polynomials
• Some symmetric semi-classical orthogonal polynomials of class 0≤s≤5
• An example of nonsymmetric semi-classical form of class \(s=1\); generalization of a case of Jacobi sequence

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