| Sum of Powers of Integers: An Application of Hua's Numbers |
| Received:May 07, 2001 |
| Key Words:
formula of sum of powers of integers Hua's numbers combinatorial model Stirling numbers mathematician Hua Heng fang .
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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 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2003.04.029 |
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