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

共 23 条

[1] [Anonymous], 1953, HIGHER TRANSCENDENTA
[2] ASSOCIATED LAGUERRE AND HERMITE-POLYNOMIALS
ASKEY, R
WIMP, J
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1984, 96 : 15 - 37
[3] ASKEY R, COMMUNICATION
[4] Askey R., 1984, MEM AM MATH SOC, P300
[5] Atkinson FV., 1964, DISCRETE CONTINUOUS
[6] Chihara T.S, 1962, T AM MATH SOC, V104, P1
[7] Chihara TS., 1978, INTRO ORTHOGONAL POL
[8] ERDELYI A, 1954, HIGHER TRANSCENDENTA, V2
[9] Freud G., 1971, ORTHOGONAL POLYNOMIA
[10] HAHN W, 1940, DTSCH MATH, V5, P373

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