A DISCRETE APPROACH TO MONOTONICITY OF ZEROS OF ORTHOGONAL POLYNOMIALS

被引：30

作者：

ISMAIL, MEH ^{[1
]}

MULDOON, ME ^{[1
]}

机构：

[1] YORK UNIV,DEPT MATH,N YORK M3J 1P3,ONTARIO,CANADA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1991年 / 323卷 / 01期

关键词：

ORTHOGONAL POLYNOMIALS; ZEROS; MONOTONICITY; RECURRENCE RELATIONS; JACOBI MATRICES;

D O I：

10.2307/2001616

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the monotonicity with respect to a parameter of zeros of orthogonal polynomials. Our method uses the tridiagonal (Jacobi) matrices arising from the three-term recurrence relation for the polynomials. We obtain new results on monotonicity of zeros of associated Laguerre, Al-Salam-Carlitz, Meixner and Pollaczek polynomials. We also derive inequalities for the zeros of the Al-Salam-Carlitz and Meixner polynomials.

引用

页码：65 / 78

页数：14

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