Geodesic
On~the asymptotics of the ratio of orthogonal polynomials.~II
Sbornik. Mathematics, Tome 46 (1983) no. 1, pp. 105-117

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Let $\mu$ be a positive measure on the circumference $\Gamma=\{z:|z|=1\}$ and let $\mu'=\dfrac{d\mu}{d\theta}>0$ almost everywhere on $\Gamma$. Let $\Phi_n(z)=z^n+\cdots$ be the orthogonal polynomials corresponding to $\mu$, and let $a_n=-\overline{\Phi_{n+1}(0)}$ be their parameters. Then $\lim\limits_{n\to\infty}a_n=0$. Bibliography: 5 titles. 
@article{SM_1983_46_1_a4,
     author = {E. A. Rakhmanov},
     title = {On~the asymptotics of the ratio of orthogonal {polynomials.~II}},
     journal = {Sbornik. Mathematics},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_46_1_a4/}
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E. A. Rakhmanov. On~the asymptotics of the ratio of orthogonal polynomials.~II. Sbornik. Mathematics, Tome 46 (1983) no. 1, pp. 105-117. http://geodesic.mathdoc.fr/item/SM_1983_46_1_a4/