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
收藏
页码：2161 / 2167
页数：7
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