| Stirling数的概率表示和应用 |
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| 引用本文： | 孙平,王天明.Stirling数的概率表示和应用[J].数学学报,1998,41(2):281-290. |
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| 作者姓名： | 孙平 王天明 |
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| 作者单位： | 大连理工大学数学科学研究所 |
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| 摘 要： | 本文证明了第二类Ｓｔｉｒｌｉｎｇ数Ｓ（ｎ，ｋ）和第一类Ｓｔｉｒｌｉｎｇ数ｓ（ｎ，ｋ）都是常见的随机变量和的矩，从而使概率论的方法和技巧，在组合和式计算、恒等式的发现与证明以及渐近估计等方面得到许多新的结果．
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| 关 键 词： | Stirling数，随机变量，矩 |
| 收稿时间： | 1997-3-25 |
Probabilistic Representations of Stirling Numbers with Applications |
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| Sun Ping,Wang Tianming.Probabilistic Representations of Stirling Numbers with Applications[J].Acta Mathematica Sinica,1998,41(2):281-290. |
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| Authors: | Sun Ping Wang Tianming |
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| Institution: | Sun Ping Wang Tianming ( Institute of Mathematical Sciences of Dalian University of Technology, Dalian 116024, China ) |
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| Abstract: | In this paper, we prove that the Stirling numbers of the first and second types both are moment of sum of common random variables, and make use of the probabilistic methods and skills to the computation of combinatorical sums, discovery and proof of combinatorial identities, and asymptotic estimation of combinatorial sums. As a result of the applications, many new results are obtained. |
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| Keywords: | Stirling number Random variable Moment |
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