On extreme zeros of classical orthogonal polynomials

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:193

Article

Krasikov, Ilia

关键词: orthogonal polynomials;    Laguerre polynomials;    Jacobi polynomials;    zeros;   

DOI  :  10.1016/j.cam.2005.05.029

来源: Elsevier

【 摘 要 】

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 a high precision. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free