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 On a conjecture of A. Magnus concerning the asymptotic behavior of the recurrence coefficients of the generalized Jacobi polynomials
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/6926

title: On a conjecture of A. Magnus concerning the asymptotic behavior of the recurrence coefficients of the generalized Jacobi polynomials
authors: Ana Pilar Foulquie Moreno
Vitor Luis Pereira de Sousa
Andrei Martínez Finkelshtein
keywords: Orthogonal polynomials
Asymptotics
Riemann–Hilbert method
Steepest descent
Recurrence coefficients
Generalized Jacobi weights
issue date: Apr-2010
publisher: Elsevier
abstract: In 1995, Magnus posed a conjecture about the asymptotics of the recurrence coefficients of orthogonal polynomials with respect to Jacobi weights with an algebraic singularity combined with a jump. We show rigorously that Magnus’ conjecture is correct even in a more general situation, when the weight above has an extra factor, which is analytic in a neighborhood of the interval of orthogonality and positive on that interval. The proof is based on the steepest descendent method of Deift and Zhou applied to the non-commutative Riemann–Hilbert problem characterizing the orthogonal polynomials. A feature of this situation is that the local analysis at has to be carried out in terms of confluent hypergeometric functions.
URI: http://hdl.handle.net/10773/6926
ISSN: 0021-9045
publisher version/DOI: dx.doi.org/10.1016/j.jat.2009.08.006
source: Journal of Approximation Theory
appears in collectionsMAT - Artigos

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