Geodesic
An asymptotic formula for polynomials orthonormal with respect to a~varying weight.~II
Sbornik. Mathematics, Tome 205 (2014) no. 9, pp. 1334-1356

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This paper gives a proof of the theorem announced by the authors in the preceding paper with the same title. The theorem states that asymptotically the behaviour of the polynomials which are orthonormal with respect to the varying weight $e^{-2nQ(x)}p_g(x)/\sqrt{\prod_{j=1}^{2p}(x-e_j)}$ coincides with the asymptotic behaviour of the Nuttall psi-function, which solves a special boundary-value problem on the relevant hyperelliptic Riemann surface of genus $g=p-1$. Here $e_1$, $Q(x)=x^{2m}+\dotsb$ is a monic polynomial of even degree $2m$ and $p_g$ is a certain auxiliary polynomial of degree $p-1$. Bibliography: 23 titles.
Keywords: varying weight, strong asymptotics
Mots-clés : orthonormal polynomials, uniform distributions. 
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     author = {A. V. Komlov and S. P. Suetin},
     title = {An asymptotic formula for polynomials orthonormal with respect to a~varying {weight.~II}},
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A. V. Komlov; S. P. Suetin. An asymptotic formula for polynomials orthonormal with respect to a~varying weight.~II. Sbornik. Mathematics, Tome 205 (2014) no. 9, pp. 1334-1356. http://geodesic.mathdoc.fr/item/SM_2014_205_9_a4/