Chebyshev polynomials on circular arcs

被引：4

作者：

Schiefermayr, Klaus ^{[1
]}

机构：

[1] Univ Appl Sci Upper Austria, Sch Engn, Campus Wels, Wels, Austria

来源：

ACTA SCIENTIARUM MATHEMATICARUM | 2019年 / 85卷 / 3-5期

关键词：

Chebyshev polynomials; circular arc; Jacobian elliptic function; Jacobian theta function; DEGENERATING BEHAVIOR;

D O I：

10.14232/actasm-018-343-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give an explicit representation of the complex Chebyshev polynomials on a given arc of the unit circle (in the complex plane) in terms of real Chebyshev polynomials on two symmetric intervals (on the real line). The real Chebyshev polynomials, for their part, can be expressed via a conformal mapping with the help of Jacobian elliptic and theta functions, which goes back to the work of Akhiezer in the 1930's.

引用

页码：629 / 649

页数：21

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