Combinatorial trigonometry with Chebyshev polynomials

被引：14

作者：

Benjamin, Arthur T. ^{[1
]}

Ericksen, Larry ^{[2
]}

Jayawant, Pallavi

Shattuck, Mark ^{[3
]}

机构：

[1] Harvey Mudd Coll, Dept Math, Claremont, CA 91711 USA

[2] Bates Coll, Dept Math, Lewiston, ME 04240 USA

[3] Univ Tennessee, Dept Math, Knoxville, TN 37006 USA

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2010年 / 140卷 / 08期

关键词：

Chebyshev polynomials; Combinatorial proof; Tiling;

D O I：

10.1016/j.jspi.2010.01.011

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We provide a combinatorial proof of the trigonometric identity cos(n theta) = T-n(cos theta), where T-n is the Chebyshey polynomial of the first kind. We also provide combinatorial proofs of other trigonometric identities, including those involving Chebyshev polynomials of the second kind. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：2157 / 2160

页数：4

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