| 华蘅芳数在幂和问题中的新应用 |
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| 引用本文： | 罗见今. 华蘅芳数在幂和问题中的新应用[J]. 数学研究及应用, 2003, 23(4): 750-756 |
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| 作者姓名： | 罗见今 |
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| 作者单位： | 内蒙古师范大学科学史研究所,内蒙古,呼和浩特,010022 |
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| 摘 要： | 自然效的幂和问题具有悠久的历史,亦不乏现代的兴趣.一般学者不了解清代数学家华蘅芳的成果.本文改进了华氏数的定义;针对该问题建立了新的取盒-放球模型,给出幂和的组合解释;应用华氏数获得了简捷的幂和公式.文末介绍了华氏数的历史来源.
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| 关 键 词： | 自然效的幂的和 华氏数 组合模型 斯特灵数 华蘅芳. |
| 文章编号： | 1000-341X(2003)04-0750-07 |
| 收稿时间： | 2001-05-07 |
| 修稿时间： | 2001-05-07 |
Sum of Powers of Integers: An Application of Hua''s Numbers |
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| LUO Jian-jin. Sum of Powers of Integers: An Application of Hua''s Numbers[J]. Journal of Mathematical Research with Applications, 2003, 23(4): 750-756 |
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| Authors: | LUO Jian-jin |
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| Affiliation: | Institute of the History of Science, Inner Mongolia Normal University, Huhhot 010022, China |
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| Abstract: | Hua Heng-fang (1833-1902) was a famous mathematician in the end of Qing Dynasty. In. his book Ji Jiao Shu (A Method of Finite Difference, 1870') Hua gave a formula of sum of powers of natural numbers using Hua's numbers. The study on sum of powers of natural numbers has a long history and a common interest today. Hua's numbers have good qualities but are not known by many mathematicians. Awaked by Hua's method only change one sign in Hua's definition and get a new formula of sum of powers of integer in this paper. This formula is very simple, and has some combinatorial significance. A box-taking and boll-putting combinatorial model is established also. |
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| Keywords: | formula of sum of powers of integers Hua's numbers combinatorial model Stirling numbers mathematician Hua Heng-fang . |
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