| Product of Uniform Distribution and Stirling Numbers of the First Kind |
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| 作者姓名： | Ping SUN |
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| 作者单位： | Department of Mathematics, Northeastern University, Shenyang 110004, P. R. China |
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| 基金项目： | This work is supported by the Mathematical Tianyuan Foundation （Grant No. A0324645） of China |
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| 摘 要： | Let Vk=u1u2……uk, ui＇s be i.i.d - U（0, 1）, the p.d.f of 1 - Vk＋l 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 Stifling series are established, and the Euler＇s result for ∑ Hn/n^k-l, k ≥ 3 is given a new probabilistic proof.
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| 关 键 词： | 母函数 一致分布 Riemann函数 组合分析 |
| 收稿时间： | 2004-02-25 |
| 修稿时间： | 2004-02-252005-02-17 |
Product of Uniform Distribution and Stirling Numbers of the First Kind |
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| Ping SUN.Product of Uniform Distribution and Stirling Numbers of the First Kind[J].Acta Mathematica Sinica,2005,21(6):1435-1442. |
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| Authors: | Ping Sun |
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| Institution: | (1) Department of Mathematics, Northeastern University, Shenyang 110004, P. R. China |
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| Abstract: | Let V
k
= u
1
u
2 ⋯ u
k
, u
i
's be i.i.d ∼ U(0, 1), the p.d.f of 1−V
k+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 ∑H
n
/n
k−1, k ≥ 3 is given a new probabilistic proof.
This work is supported by the Mathematical Tianyuan Foundation (Grant No. A0324645) of China |
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| Keywords: | Stirling numbers generating function uniform distribution moment Riemann zeta function |
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