On extreme zeros of classical orthogonal polynomials

Details On extreme zeros of classical orthogonal polynomials On extreme zeros of classical orthogonal polynomials

2003-06-19

arxiv.org/abs/math/0306286v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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 $x_1 B,$ 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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