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

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.

Bibliographic Details
Authors: Adell, José A., Lekuona, Alberto
Format: article
Status:Published version
Publication Date:2019
Country:España
Institution:Universidad de Zaragoza
Repository:Zaguán. Repositorio Digital de la Universidad de Zaragoza
OAI Identifier:oai:zaguan.unizar.es:86233
Online Access:http://zaguan.unizar.es/record/86233
Access Level:Open access
Description
Summary: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.