Freud equations for Legendre polynomials on a circular arc and solution of the Grünbaum–Delsarte–Janssen–Vries problem |
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| Authors: | Alphonse P. Magnus |
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| Affiliation: | Institut Mathématique, Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium |
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| Abstract: | One establishes inequalities for the coefficients of orthogonal polynomialswhich are orthogonal with respect to a constant weight on the arc of the unit circle S={eiθ,απ<θ<2π-απ}, with 0<α<1. Recurrence relations (Freud equations), and differential relations are used. Among other results, it is shown that Φn(0)>0,n=1,2,… |
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| Keywords: | Unit circle orthogonal polynomials |
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