A probabilistic generalization of the Stirling numbers of the second kind

JOURNAL OF NUMBER THEORY

卷:194

Article

Adell, Jose A.¹  Lekuona, Alberto¹ 

[1] Univ Zaragoza, Fac Ciencias, Dept Metodos Estadist, E-50009 Zaragoza, Spain

关键词: Generalized Stirling numbers of the second kind;    Sum of powers formula;    Difference operators;    Bell polynomials;    Polylogarithms;    Appell polynomials;   

DOI  :  10.1016/j.jnt.2018.07.003

来源: Elsevier

【 摘 要 】

Associated to each random variable Y satisfying appropriate moment conditions, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers are provided. As far as their applications are concerned, attention is focused in extending in various ways the classical formula for sums of powers on arithmetic progressions. Illustrations involving rising factorials, Bell polynomials, polylogarithms, and a certain class of Appell polynomials, in connection with appropriate random variables Y in each case, are discussed in detail. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free