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

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spelling	doaj-d4a795b65a72413aa52e807b26dca9762020-11-25T02:12:57ZengSpringerOpenAdvances in Difference Equations1687-18472019-09-012019111110.1186/s13662-019-2337-4Explicit expressions and integral representations for the Stirling numbers. A probabilistic approachJosé A. Adell0Alberto Lekuona1Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de ZaragozaDepartamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de ZaragozaAbstract 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.http://link.springer.com/article/10.1186/s13662-019-2337-4Stirling numbersExplicit expressionIntegral representationMomentCharacteristic functionGeneralized difference operator
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	José A. Adell Alberto Lekuona
spellingShingle	José A. Adell Alberto Lekuona Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach Advances in Difference Equations Stirling numbers Explicit expression Integral representation Moment Characteristic function Generalized difference operator
author_facet	José A. Adell Alberto Lekuona
author_sort	José A. Adell
title	Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach
title_short	Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach
title_full	Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach
title_fullStr	Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach
title_full_unstemmed	Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach
title_sort	explicit expressions and integral representations for the stirling numbers. a probabilistic approach
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2019-09-01
description	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.
topic	Stirling numbers Explicit expression Integral representation Moment Characteristic function Generalized difference operator
url	http://link.springer.com/article/10.1186/s13662-019-2337-4
work_keys_str_mv	AT joseaadell explicitexpressionsandintegralrepresentationsforthestirlingnumbersaprobabilisticapproach AT albertolekuona explicitexpressionsandintegralrepresentationsforthestirlingnumbersaprobabilisticapproach
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Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach

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