| 自然数方幂和的一个计算通式 |
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| 引用本文： | 向明华,王如森. 自然数方幂和的一个计算通式[J]. 哈尔滨工程大学学报, 1989, 0(3) |
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| 作者姓名： | 向明华 王如森 |
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| 作者单位： | 哈尔滨船舶工程学院航天工程系(向明华)，哈尔滨船舶工程学院航天工程系(王如森) |
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| 摘 要： | 本文从差分方程理论出发,讨论了自然数方幂求和,文中只运用了简单的初等推导,所得结果较金治明在1984年得到的结果更简单实用,同时还得到了分析中有重要应用的Bernoulli数的显式递推计算公式.
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| 关 键 词： | 自然数方幂和 差分方程 特征方程 递推公式 Bernoulli数 |
A General Formula of Calculating the Sum of the Powers of the Natural Numbers |
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| Xiang Minghua ,Wang Rusen. A General Formula of Calculating the Sum of the Powers of the Natural Numbers[J]. Journal of Harbin Engineering University, 1989, 0(3) |
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| Authors: | Xiang Minghua Wang Rusen |
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| Affiliation: | Dept. of Aerospace Eng. |
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| Abstract: | The sum of the powers of the Natural Numbers is researched with the difference-equation theory.Only the elementary operations are used, but the result is better than that gainned by Gin Zhiming in 1984.Furtherm-ore, a explicit recurrence formula to calculate Bernoulli numbers is found which are of importance in the mathematical analysis. |
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| Keywords: | sum of the powers of the natural numbers difference equation characteristic equation recurrence formula Bernoulli number |
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