Geodesic
Nuttall's integral equation and Bernshtein's asymptotic formula for a~complex weight
Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1215-1234

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We obtain Nuttall's integral equation provided that the corresponding complex-valued function $\sigma(x)$ does not vanish and belongs to the Dini–Lipschitz class. Using this equation, we obtain a complex analogue of Bernshtein's classical asymptotic formulae for polynomials orthogonal on the closed unit interval $\Delta=[-1,1]$ with respect to a complex-valued weight $h(x)=\sigma(x)/\sqrt{1-x^2}$.
Keywords: Padé polynomials, strong asymptotics, Bernshtein's formula, Nuttall's method.
Mots-clés : orthogonal polynomials 
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N. R. Ikonomov; R. K. Kovacheva; S. P. Suetin. Nuttall's integral equation and Bernshtein's asymptotic formula for a~complex weight. Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1215-1234. http://geodesic.mathdoc.fr/item/IM2_2015_79_6_a4/