Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach

Author:

Adell José A.,Lekuona Alberto

Abstract

Abstract We show that the Stirling numbers of the first and second kind can be represented in terms of moments of appropriate random variables. This allows us to obtain, in a unified way, a variety of old and new explicit expressions and integral representations of such numbers.

Funder

Ministerio de Ciencia, Innovación y Universidades

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A probabilistic generalization of the Bell polynomials;The Journal of Analysis;2023-09-06

2. Explicit estimates for Comtet numbers of the first kind;Journal of Computational and Applied Mathematics;2022-11

3. Explicit upper bounds for the Stirling numbers of the first kind;Journal of Combinatorial Theory, Series A;2022-11

4. On the Uniqueness Conjecture for the Maximum Stirling Numbers of the Second Kind;Results in Mathematics;2021-04-15

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