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On extreme zeros of classical orthogonal polynomials

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 نشر من قبل Ilia Krasikov
 تاريخ النشر 2003
  مجال البحث
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 تأليف Ilia Krasikov




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Let $x_1$ and $x_k$ be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree $k.$ We shall establish sharp inequalities of the form $x_1 <A, x_k >B,$ which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical orthogonal polynomials with the relative precision, roughly speaking, $O(k^{-2/3}).$



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