On the Chebyshev polynomials

被引：0
|
作者：
Boyadjiev, L [1 ]
Scherer, R
机构：
[1] Univ Karlsruhe TH, Math Inst 2, D-76128 Karlsruhe, Germany
[2] Univ Karlsruhe TH, Inst Prakt Math, D-76128 Karlsruhe, Germany
来源：
KUWAIT JOURNAL OF SCIENCE & ENGINEERING | 2001年 / 28卷 / 02期
关键词：
Chebyshev polynomial; function of second kind; Gauss quadrature; quadrature error estimates; series expansions;
D O I：
暂无
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We put special attention in this paper on the Chebyshev polynomials of the fourth kind because they are much less known and less studied than others. The representation problem of analytic functions in series of such polynomials is considered, and the important role of the Chebyshev functions of the second kind in solving them is emphasized. For analytic functions, the remainder term of Gauss quadrature rules can be represented as a contour integral with a complex kernel function. The kernel function related to the Gauss quadrature for Chebyshev polynomials of the fourth kind is especially studied on elliptic contours and the points of its maximum are specified.
引用
收藏
页码：227 / 240
页数：14
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