SOME NEW ASYMPTOTIC PROPERTIES FOR THE ZEROS OF JACOBI, LAGUERRE, AND HERMITE-POLYNOMIALS

被引：40

作者：

DETTE, H ^{[1
]}

STUDDEN, WJ ^{[1
]}

机构：

[1] PURDUE UNIV, DEPT STAT, W LAFAYETTE, IN 47907 USA

来源：

CONSTRUCTIVE APPROXIMATION | 1995年 / 11卷 / 02期

关键词：

JACOBI POLYNOMIALS; LAGUERRE POLYNOMIALS; HERMITE POLYNOMIALS; ASYMPTOTIC ZERO DISTRIBUTION; CHAIN SEQUENCES;

D O I：

10.1007/BF01203416

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For the generalized Jacobi, Laguerre, and Hermite polynomials P-n((alpha n,beta n))(x), L(n)((alpha n))(X), H-n((gamma n))(X) the limit distributions of the zeros are found, when the sequences alpha(n) or beta(n) tend to infinity with a larger order than n. The derivation uses special properties of the sequences in the corresponding recurrence formulas. The results are used to give second-order approximations for the largest and smallest zero which improve (and generalize) the limit statements in a paper by Moak, Saff, and Varga [11].

引用

页码：227 / 238

页数：12

共 16 条

[1] ON ASYMPTOTICS OF JACOBI-POLYNOMIALS [J].