On extreme zeros of classical orthogonal polynomials
Copyright policy )On extreme zeros of classical orthogonal polynomials
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, $O(k^{-2/3}).$
- Brunel University London United Kingdom
- Department of Mathematical Sciences Russian Federation
- Brunel University United Kingdom
Zeros, Computational Mathematics, Orthogonal polynomials, Mathematics - Classical Analysis and ODEs, Applied Mathematics, Jacobi polynomials, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Laguerre polynomials, 33C45
Zeros, Computational Mathematics, Orthogonal polynomials, Mathematics - Classical Analysis and ODEs, Applied Mathematics, Jacobi polynomials, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Laguerre polynomials, 33C45
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