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| 摘要: |
| 本文研究了Chebyshef多项式的一类幂和问题.利用初等方法以及Chebyshef多项式的性质,获得了一些有趣的恒等式,推广了Melham关于Lucas数的奇数次幂和的猜想. |
| 关键词: Chebyshef多项式 Fibonacci数 Lucas数 恒等式 Melham猜想 |
| DOI： |
| 分类号:O156.4 |
| 基金项目:Supported by Scientiflc Research Foundation of Shaanxi Provincial Education Department(2013JK0561); Doctor Foundation of Xi'an Medical University (2012DOC14). |
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| SOME IDENTITIES RELATED TO CHEBYSHEFPOLYNOMIALS AND THEIR APPLICATIONS |
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PAN Xiao-wei
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| Abstract: |
| In this article, we study a kind of sum powers of Chebyshef polynomials. By using elementary method and the properties of the Chebyshef polynomials, several new identities are obtained, which generalizes Melham's conjecture on sums of odd powers of Lucas numbers. |
| Key words: Chebyshef polynomials Fibonacci numbers Lucas numbers identity Melham's conjectures |
