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Freud equations for Legendre polynomials on a circular arc and solution of the Grunbaum-Delsarte-Janssen-Vries problem

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Magnus, AP.

One establishes inequalities for the coefficients of orthogonal polynomials Phi(n)(z) = z(n) + xi(n)z(n-1) +...+ Phi(n)(0), n = 0, 1,.... which are orthogonal with respect to a constant weight on the arc of the unit circle S={e(io), alpha pi < 0 < 2 pi-alpha pi), with 0 < alpha < 1. Recurrence relations (Freud equations), and differential relations are used. Among other results, it is shown that Phi(n)(0) > 0, n = 1, 2.... (C) 2005 Elsevier Inc. All rights reserved.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2006
Language Anglais
Journal information "Journal of Approximation Theory" - Vol. 139, no. 1-2, p. 75-90 (2006)
Peer reviewed yes
Publisher Academic Press Inc Elsevier Science (San Diego)
issn 0021-9045
e-issn 1096-0430
Publication status Publié
Affiliation UCL
Keywords unit circle orthogonal polynomials
Links
Bibliographic reference Magnus, AP.. Freud equations for Legendre polynomials on a circular arc and solution of the Grunbaum-Delsarte-Janssen-Vries problem. In: Journal of Approximation Theory, Vol. 139, no. 1-2, p. 75-90 (2006)
Permanent URL http://hdl.handle.net/2078.1/38507