Combinatorially composing Chebyshev polynomials

被引：4

作者：

Benjamin, Arthur T. ^{[1
]}

Walton, Daniel ^{[2
]}

机构：

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

[2] Univ Calif Los Angeles, Dept Atmospher & Ocean Sci, Los Angeles, CA 90095 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.2010.01.012

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 present a combinatorial proof of two fundamental composition identities associated with Chebyshev polynomials. Namely, for all m, n >= 0, T(m)(T(n)(x)) = T(mn)(x) and U(m-1) (T(n)(x))U(n-1)(x) = U(mn-1)(x). (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：2161 / 2167

页数：7

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