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This article is cited in 109 scientific papers (total in 109 papers)
On the asymptotics of the ratio of orthogonal polynomials
E. A. Rakhmanov
Abstract:
Conditions are obtained for the existence of “exterior” asymptotics for orthogonal polynomials. In particular, it is shown that if $\rho'>0$ almost everywhere on the interval $[-1,1]$ ($\rho(x)$ is a nondecreasing function on $[-1,1]$), then for the corresponding orthonormal polynomials the relation $\frac{P_{n+1}(z)}{P_n(z)}\rightrightarrows z+\sqrt{z^2-1}$ holds on compact subsets of $\mathbf C\setminus[-1,1]$. The branch of the square root is chosen so that $|z+\sqrt{z^2-1} |>1$ in the region described.
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Mathematics of the USSR-Sbornik, 1977, 32:2, 199–213
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UDC:
517.5
MSC: 30A84, 33A65
Received: 13.10.1976
Citation:
E. A. Rakhmanov, “On the asymptotics of the ratio of orthogonal polynomials”, Mat. Sb. (N.S.), 103(145):2(6) (1977), 237–252; Math. USSR-Sb., 32:2 (1977), 199–213
Citation in format AMSBIB
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\jour Math. USSR-Sb.
\yr 1977
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\pages 199--213
\crossref{https://doi.org/10.1070/SM1977v032n02ABEH002377}
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