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.
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This work is supported by the Mathematical Tianyuan Foundation (Grant No. A0324645) of China
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Sun, P. Product of Uniform Distribution and Stirling Numbers of the First Kind. Acta Math Sinica 21, 1435–1442 (2005). https://doi.org/10.1007/s10114-005-0631-4
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DOI: https://doi.org/10.1007/s10114-005-0631-4