Stirling数的概率表示和应用  

Probabilistic Representations of Stirling Numbers with Applications

作　　者：孙平[1] 王天明[1] 

机构地区：[1]大连理工大学数学科学研究所

出　　处：《数学学报（中文版）》1998年第2期281-290,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

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．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.

关 键 词：STIRLING数 随机变量 概率表示 渐近估计 

分 类 号：O157.1[理学—数学]