| 关于Vandermonde恒等式衍变式的推导与应用 |
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| 引用本文： | 杜瑞卿,王骁力. 关于Vandermonde恒等式衍变式的推导与应用[J]. 南阳师范学院学报, 2013, 12(9): 11-15 |
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| 作者姓名： | 杜瑞卿 王骁力 |
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| 作者单位： | 1. 南阳师范学院生命科学与技术学院,河南南阳,473061
2. 南阳师范学院数学与统计学院,河南南阳,473061 |
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| 基金项目： | 河南省科技厅自然科学基金项目 |
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| 摘 要： | 根据Vandermonde恒等式,提出了4个衍变式:①∑ki=0CinCk-in+k-1-i,②∑ki=1(-1)i-1CinCk-in+k-1-i,③∑ni=0Cia+iCn-ib+n-i,④∑ni=0(-1)iCia+iCn-ib+n-i,利用母函数法或行列式法进行了推导,得出了4个新的恒等式,并利用恒等式证明了杨辉三角子行列式.
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| 关 键 词： | vandermonde恒等式 衍变 母函数法 行列式法 |
The proof and application of evolution identities of Vandermonde's identity |
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| DU Rui-qing , WANG Xiao-li. The proof and application of evolution identities of Vandermonde's identity[J]. Journal of Nanyang Teachers College, 2013, 12(9): 11-15 |
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| Authors: | DU Rui-qing WANG Xiao-li |
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| Affiliation: | 1. School of Life Science and Technology, Nanyang Normal University, Nanyang 473061, China; 2. School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China) |
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| Abstract: | Firstly, four evolution identities of Vandermonde＇ s idenltity were put in the paper.①∑i=0^k Cn^iCn＋k-1-i^k-i,②∑i=1^k（-1）^i-1Cn^iCn＋k-1-i^k-i,③∑i=0^nCa＋i^iCb＋n-i^n-i④∑i=0^n（-1）^iCa＋i^iCb＋n-1^n-iThen four new identities were proved by generating function method or determinant method. Using these identities, a proof of a sub-determinant of Yang Hui＇s triangle was given. |
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| Keywords: | Vandermonde＇ s identity evolution generating function method determinant method |
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