Product of uniform distribution and Stirling numbers of the first kind

被引：12
|
作者：
Sun, P [1 ]
机构：
[1] Northeastern Univ, Dept Math, Shenyang 110004, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2005年 / 21卷 / 06期
关键词：
Stirling numbers; generating function; uniform distribution; moment; Riemann zeta function;
D O I：
10.1007/s10114-005-0631-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let V-k = mu(1)mu(2)center dot center dot center dot mu(k), u(i)'s be i.i.d similar to U(0, 1), the p.d.f of 1 - Vk+1 be the GF of the unsigned Stirling numbers of the first kind s(n, k). This paper discusses the applications of uniform distribution to combinatorial. analysis and Riemann zeta function; several identities of Stirling series are established, and the Euler's result for Sigma H-n/n(k-1), k >= 3 is given a new probabilistic proof.
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页码：1435 / 1442
页数：8
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