Geodesic
Strong asymptotics of polynomials orthogonal with respect to
Sbornik. Mathematics, Tome 200 (2009) no. 1, pp. 77-93

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For polynomials orthogonal with respect to a complex-valued weight on the closed interval $\Delta=[-1,1]$ a strong asymptotic formula in a neighbourhood of $\Delta$ is obtained. In particular, for the ‘trigonometric’ weight $\rho_0(x)=e^{ix}$, $x\in\Delta$, this formula yields a description of the asymptotic behaviour of each of the $n$ zeros of the $n$th orthogonal polynomial as $n\to\infty$. This strong asymptotic formula is deduced on the basis of Nuttall's singular integral equation. Bibliography: 28 titles.
Keywords: strong asymptotics.
Mots-clés : Padé approximants, orthogonal polynomials 
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S. P. Suetin. Strong asymptotics of polynomials orthogonal with respect to. Sbornik. Mathematics, Tome 200 (2009) no. 1, pp. 77-93. http://geodesic.mathdoc.fr/item/SM_2009_200_1_a2/