| 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 |
| 华蘅芳数在幂和问题中的新应用 |
| Sum of Powers of Integers: An Application of Hua's Numbers |
| 投稿时间：2001-05-07 |
| DOI：10.3770/j.issn:1000-341X.2003.04.029 |
| 中文关键词: 自然效的幂的和 华氏数 组合模型 斯特灵数 华蘅芳. |
| 英文关键词:formula of sum of powers of integers Hua's numbers combinatorial model Stirling numbers mathematician Hua Heng fang . |
| 基金项目: |
|
| 摘要点击次数: 2148 |
| 全文下载次数: 1126 |
| 中文摘要: |
| 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. |
| 英文摘要: |
| 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 math ematicians. Awaked by Hua's method only change one s ign in Hua's definition and get a new formula of sum of powers of integer in th is paper. This formula is very simple, and has some combinatorial sign ificance. A box taking and boll putting combinatorial model is established also. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
