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

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

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.

Bibliographic Details
Main Authors: José A. Adell, Alberto Lekuona
Format: Article
Language:English
Published: SpringerOpen 2019-09-01
Series:Advances in Difference Equations
Subjects:
Stirling numbers
Explicit expression
Integral representation
Moment
Characteristic function
Generalized difference operator
Online Access:http://link.springer.com/article/10.1186/s13662-019-2337-4
Description
Summary: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.
ISSN:1687-1847

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