On extreme zeros of classical orthogonal polynomials

Ilia Krasikov

doi:10.1016/j.cam.2005.05.029

On extreme zeros of classical orthogonal polynomials

Ilia Krasikov^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let x₁ 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 x₁ < 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 a high precision.

Original language	English
Pages (from-to)	168-182
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	193
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2005.05.029
State	Published - 15 Aug 2006
Externally published	Yes

Keywords

Jacobi polynomials
Laguerre polynomials
Orthogonal polynomials
Zeros

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10.1016/j.cam.2005.05.029

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abstract = "Let x1 and xk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree k. We shall establish sharp inequalities of the form x1 < A, xk > 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 a high precision.",

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AB - Let x1 and xk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree k. We shall establish sharp inequalities of the form x1 < A, xk > 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 a high precision.

KW - Jacobi polynomials

KW - Laguerre polynomials

KW - Orthogonal polynomials

KW - Zeros

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On extreme zeros of classical orthogonal polynomials

Abstract

Keywords

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