A new property of a class of Jacobi polynomials

被引：8

作者：

Csordas, G ^{[1
]}

Charalambides, M

Waleffe, F

机构：

[1] Univ Hawaii, Dept Math, Honolulu, HI 96822 USA

[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 133卷 / 12期

关键词：

Jacobi and Bessel polynomials; stability; real zeros of polynomials;

D O I：

10.1090/S0002-9939-05-07898-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Polynomials whose coefficients are successive derivatives of a class of Jacobi polynomials evaluated at x = 1 are stable. This yields a novel and short proof of the known result that the Bessel polynomials are stable polynomials. Stability-preserving linear operators are discussed. The paper concludes with three open problems involving the distribution of zeros of polynomials.

引用

页码：3551 / 3560

页数：10

共 23 条

[1]

[Anonymous], 1974, COLLECTED PAPERS

[2]

[Anonymous], 1964, Handbook of mathematical functions

[3]

[Anonymous], 1999, ENCY MATH APPL

[4]

Canuto C., 2012, Spectral Methods: Fundamentals in Single Domains

[5]

Chihara T. S., 1978, MATH ITS APPL, V13

[6]

CRAVEN T, 1983, T AM MATH SOC, V278, P415

[7]

CRAVEN T, IN PRESS VALUE DISTR

[8]

Erdelyi A., 1953, HIGHER TRANSCENDENTA, VII

[9] Hadamard products of stable polynomials are stable [J].

Garloff, J ;

Wagner, DG .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 202 (03) :797-809

[10] THE SPECTRUM OF THE TSCHEBYSCHEV COLLOCATION OPERATOR FOR THE HEAT-EQUATION [J].

GOTTLIEB, D ;

LUSTMAN, L .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (05) :909-921

← 1 2 3 →