BOUND ON THE EXTREME ZEROS OF ORTHOGONAL POLYNOMIALS

被引：78

作者：

ISMAIL, MEH ^{[1
]}

LI, X ^{[1
]}

机构：

[1] UNIV CENT FLORIDA,DEPT MATH,ORLANDO,FL 32816

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 115卷 / 01期

关键词：

BOUNDS; CHAIN SEQUENCES; CHIHARA-WALL-WETZEL THEOREM; LAGUERRE POLYNOMIALS; LARGEST ZERO; MEIXNER POLYNOMIALS; MEIXNER-POLLACZEK POLYNOMIALS; RECURRENCE RELATIONS; SMALLEST ZERO;

D O I：

10.2307/2159575

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using chain sequences we formulate a procedure to find upper (lower) bounds for the largest (smallest) zero of orthogonal polynomials in terms of their recurrence coefficients. We also apply our method to derive bounds for extreme zeros of the Laguerre, associated Laguerre, Meixner, and Meixner-Pollaczek polynomials. In addition, we consider bounds for the extreme zeros of Jacobi polynomials of degree n and parameters a(n) and b(n).

引用

页码：131 / 140

页数：10

共 19 条

[1] ALSALAM WA, 1990, NATO ADV SCI I C-MAT, V294, P1
[2] ANDREWS GE, 1985, LECT NOTES MATH, V1171, P36
[3] SET OF ORTHOGONAL POLYNOMIALS THAT GENERALIZE THE RACAH COEFFICIENTS OR 6-J SYMBOLS
ASKEY, R
WILSON, J
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1979, 10 (05) : 1008 - 1016
[4] ASSOCIATED LAGUERRE AND HERMITE-POLYNOMIALS
ASKEY, R
WIMP, J
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1984, 96 : 15 - 37
[5] ASKEY R, 1985, MEM AM MATH SOC, V319
[6] ON ASYMPTOTICS OF JACOBI-POLYNOMIALS
CHEN, LC
ISMAIL, MEH
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1991, 22 (05) : 1442 - 1449
[7] Chihara T.S, 1962, T AM MATH SOC, V104, P1
[8] Chihara TS., 1978, INTRO ORTHOGONAL POL
[9] Erdelyi A., 1953, HIGHER TRANSCENDENTA, VII
[10] GAWRONSKI W, IN PRESS J APPROX TH

← 1 2 →