| 广义Fibonacci序列和广义Lucas序列的性质 |
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| 引用本文： | 王军霞,杨胜良.广义Fibonacci序列和广义Lucas序列的性质[J].甘肃科学学报,2009,21(4):9-12. |
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| 作者姓名： | 王军霞 杨胜良 |
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| 作者单位： | 兰州理工大学,理学院,甘肃,兰州,730050 |
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| 基金项目： | 甘肃省自然科学基金项目 |
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| 摘 要： | 研究了广义Fibonacci序列,给出了它的行列式表示.利用发生函数研究广义Fibonacci序列,得出了Fibonacci序列的一些恒等式以及此序列与第2类Chebyshev多项式的关系.在此基础上,推出了广义Lucas序列的类似性质.
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| 关 键 词： | 广义Fibonacci序列 广义Lucas序列 发生函数 Chebyshev多项式 行列式 |
Properties of the Generalized Fibonacci Sequence and Generalized Lucas Sequence |
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| WANG Jun-xia,YANG Sheng-liang.Properties of the Generalized Fibonacci Sequence and Generalized Lucas Sequence[J].Journal of Gansu Sciences,2009,21(4):9-12. |
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| Authors: | WANG Jun-xia YANG Sheng-liang |
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| Institution: | WANG Jun-xia,YANG Sheng-liang(School of Sciences,Lanzhou University of Science and Technology,Lanzhou 730050,China) |
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| Abstract: | A generalized Fibonacci sequence is introduced,and a determinant formula for the generalized Fibonacci sequence is given.Using generating functions,some identities for the generalized Fibonacci sequence and the relationship between generalized Fibonacci sequence and the second kind of Chebyshev polynomials are obtained.The similar properties for the generalized Lucas sequence are also derived. |
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| Keywords: | generalized Fibonacci sequence generalized Lucas sequence generating function Chebyshev polynomials determinant |
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