Some formulate for the Fibonacci and Lucas numbers

被引：0
|
作者：
Hu, Jiayuan [1 ]
机构：
[1] Northwest Univ, Dept Math, Xian, Shaanxi, Peoples R China
来源：
RESEARCH ON NUMBER THEORY AND SMARANDACHE NOTIONS | 2010年
关键词：
Fibonacci numbers; Lucas numbers; Chebyshev polynomials;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper mainly study some identities involving Fibonacci and Lucas numbers of interest. By using the properties of Chebyshev polynomials and combining the elementary and combinatorial method, we establish identities that Sigma(d-1)(j=0) F(n+j)F(m+j)x(j) , Sigma(d-1)(j=0) Ln+j Lm+j x(j) , Sigma F-d-1(j=0)n1+j Fn2+j Fn3+j, and Sigma L-d-1(j=0)n1+j Ln2+j Ln3+j. These identities are extensions of Sigma(d-1)(j=0) Fn+jFm+j and Sigma(d-1)(j=0) Ln+j Lm+j which have been proved by Brian Curtin before.
引用
收藏
页码：119 / 127
页数：9
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