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
收藏
页码：65 / 78
页数：14
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