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

Magnus, AP.
(2006) Journal of Approximation Theory — Vol. 139, n° 1-2, p. 75-90 (2006)

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  • Magnus, AP.
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Abstract
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.
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Magnus, AP. (2006). Freud equations for Legendre polynomials on a circular arc and solution of the Grunbaum-Delsarte-Janssen-Vries problem. Journal of Approximation Theory, 139(1-2), 75-90. https://doi.org/10.1016/j.jat.2005.04.010 (Original work published 2006)