UPPER-BOUNDS FOR THE ZEROS OF ULTRASPHERICAL POLYNOMIALS

被引：19

作者：

ELBERT, A ^{[1
]}

LAFORGIA, A ^{[1
]}

机构：

[1] UNIV PALERMO,DIPARTIMENTO MATEMAT & APPLICAZ,I-90123 PALERMO,ITALY

来源：

JOURNAL OF APPROXIMATION THEORY | 1990年 / 61卷 / 01期

关键词：

D O I：

10.1016/0021-9045(90)90025-L

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For k = 1, 2, ..., [ n 2] let xnk(λ) denote the Kth positive zero in decreasing order of the ultraspherical polynomial Pn(λ)(x). We establish upper bounds for xnk(λ). All the bounds become exact when λ = 0 and, in some cases (see case (iii) of Theorem 3.1), also when λ = 1. As a consequence of our results, we obtain for the largest zero xn1(λ)< (n2+2λn)1,2 (n+λ), λ>0.. We point out that our results remain useful for large values of λ. Numerical examples show that our upper bounds are quite sharp. © 1990.

引用

页码：88 / 97

页数：10