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Эта публикация цитируется в 109 научных статьях (всего в 109 статьях)
Об асимптотике отношения ортогональных многочленов
Е. А. Рахманов
Аннотация:
Получены условия существования “внешней” асимптотики ортогональных
многочленов. Показано, в частности, что если $\rho'>0$ почти всюду на отрезке $[-1,1]$ ($\rho(x)$ – неубывающая функция на $[-1,1]$), то для соответствующих ортонормированных многочленов справедливо соотношение $\frac{P_{n+1}(z)}{P_n(z)}\rightrightarrows z+\sqrt{z^2-1}$
внутри $\mathbf C\setminus[-1,1]$. Ветвь корня выбрана так, что $|z+\sqrt{z^2-1} |>1$ в указанной области.
Библиография: 6 названий.
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Англоязычная версия:
Mathematics of the USSR-Sbornik, 1977, 32:2, 199–213
Реферативные базы данных:
  
УДК:
517.5
MSC: 30A84, 33A65
Поступила в редакцию: 13.10.1976
Образец цитирования:
Е. А. Рахманов, “Об асимптотике отношения ортогональных многочленов”, Матем. сб., 103(145):2(6) (1977), 237–252; E. A. Rakhmanov, “On the asymptotics of the ratio of orthogonal polynomials”, Math. USSR-Sb., 32:2 (1977), 199–213
Цитирование в формате AMSBIB
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\pages 237--252
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\by E.~A.~Rakhmanov
\paper On the asymptotics of the ratio of orthogonal polynomials
\jour Math. USSR-Sb.
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\pages 199--213
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Цикл статей
Эта публикация цитируется в следующих статьяx:
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Е. А. Рахманов, “О сходимости диагональных аппроксимаций Паде”, Матем. сб., 104(146):2(10) (1977), 271–291
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