A probabilistic generalization of the Stirling numbers of the second kind

Adell, J.A. (Universidad de Zaragoza) ; Lekuona, A. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.jnt.2018.07.003

Año: 2018

Publicado en: JOURNAL OF NUMBER THEORY 194 (2018), 335-355
ISSN: 0022-314X

Factor impacto JCR: 0.684 (2018)

Categ. JCR: MATHEMATICS rank: 181 / 313 = 0.578 (2018) - Q3 - T2

Factor impacto SCIMAGO: 0.837 - Algebra and Number Theory (Q1)

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)