Geodesic
Relative asymptotics for polynomials orthogonal on the real axis
Sbornik. Mathematics, Tome 65 (1990) no. 2, pp. 505-529 Cet article a éte moissonné depuis la source Math-Net.Ru

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Given a positive Borel measure $\rho$ on the real line $\mathbf R$ and a function $g$ on $\mathbf R$, the main purpose of the paper is to prove (under certain assumptions on $\rho$) relative asymptotic formulas of the type $$ \frac{h_n(gd\rho,z)}{h_n(d\rho,z)}\underset{n\to\infty}\rightrightarrows S(g,\Omega;z),\qquad z\in\Omega, $$ where $\Omega=\{z:\operatorname{Im}z>0\}$, $S(g,\Omega;z)$ is Szegö's function corresponding to $\Omega$ and the function $g$, $h_n(gd\rho,z)$ and $h_n(d\rho,z)$ are polynomials orthonormal relative to the measures $gd\rho$ and $d\rho$ respectively. Bibliography: 15 titles. 
@article{SM_1990_65_2_a11,
     author = {G. L. Lopes},
     title = {Relative asymptotics for polynomials orthogonal on the real axis},
     journal = {Sbornik. Mathematics},
     pages = {505--529},
     year = {1990},
     volume = {65},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_65_2_a11/}
}
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G. L. Lopes. Relative asymptotics for polynomials orthogonal on the real axis. Sbornik. Mathematics, Tome 65 (1990) no. 2, pp. 505-529. http://geodesic.mathdoc.fr/item/SM_1990_65_2_a11/

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