| Fibonacci和Lucas序列的混合卷积公式 |
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| 引用本文： | 席高文. Fibonacci和Lucas序列的混合卷积公式[J]. 数学的实践与认识, 2007, 37(5): 117-124 |
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| 作者姓名： | 席高文 |
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| 作者单位： | 洛阳师范学院,数学与信息科学系,河南,洛阳,471022 |
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| 摘 要： | 通过Fibonacci序列和Lucas序列的生成函数,利用导函数的性质,得到了Fibonacci序列和Lucas序列构成的混合卷积∑a1+a2+…+ak+b1+b2+…+b1+c1+c2+…+cm=na1Fa1+1…akFak+1.Fb1…Fb1.Lc1+1…Lcm+1的计算公式.
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| 关 键 词： | Fibonacci序列 Lucas序列 生成函数 求和 数学归纳法 |
| 修稿时间： | 2005-12-19 |
Mixed-Convoluted Formulas for Fibonacci and Lucas Sequences |
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| XI Gao-wen. Mixed-Convoluted Formulas for Fibonacci and Lucas Sequences[J]. Mathematics in Practice and Theory, 2007, 37(5): 117-124 |
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| Authors: | XI Gao-wen |
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| Abstract: | By applying the generating function of Fibonacci and Lucas sequences,using the differential properties,the purpose of this paper is to give the following Mixed-Convoluted Formulas for Fibonacci and Lucas Sequences∑a1+a2+…+ak+b1+b2+…+b1+c1+c2+…+cm=na1Fa1+1…akFak+1·Fb1…Fb1·Lc1+1…Lcm+1 |
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| Keywords: | fibonacci sequences lucas sequences generating function summation induction |
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