| 涉及Fibonacci数和Lucas数的多重卷积公式 |
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| 引用本文： | 王悦.涉及Fibonacci数和Lucas数的多重卷积公式[J].淮阴师范学院学报(自然科学版),2012(1):17-21. |
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| 作者姓名： | 王悦 |
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| 作者单位： | 宁夏大学数学计算机学院;淮阴师范学院数学科学学院 |
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| 摘 要： | 根据Fibonacci数{Fn}和Lucas数{Ln}的递归关系,研究了关于Fibonacci数和Lucas数的生成函数∑∞n=1Fn2xn和∑∞n=1Ln2xn.利用第一类Stirling数和第二类Stirling数,获得了涉及Fibonacci数和Lucas数的多重卷积公式,推广了WChu的相关结论.
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| 关 键 词： | Fibonacci数 Lucas数 幂级数 多重卷积 |
Involving the Multiple Convolution Formula of Fibonacci Number and Lucas Number |
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| WANG Yue.Involving the Multiple Convolution Formula of Fibonacci Number and Lucas Number[J].Journal of Huaiyin Teachers College(Natrual Science Edition),2012(1):17-21. |
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| Authors: | WANG Yue |
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| Institution: | WANG Yue1,2(1.School of Mathematics and Computer Science,Ningxia University,Yinchuan Ningxia 75000,China)(2.School of Mathematical Science,Huaiyin Normal University,Huaian Jiangsu 223300,China) |
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| Abstract: | In this paper,it was mainly discussed the relationship of recursiveness on the basis of Fibonacci Number {Fn}and Lucas Number{Ln},researched the generating function of ∑∞n=1Fn2 xn and ∑∞n=1Ln2 xn in relation to Fibonacci Number and Lucas Number.Used the Stirling numbers of the first kind and the Stirling numbers of the second kind,got involved in the multiple convolution formula of Fibonacci Number and Lucas Number,generalized W Chu’s related conclusions. |
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| Keywords: | fibonacci number lucas number power serues multiple convolution |
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