000130437 001__ 130437 000130437 005__ 20240125162930.0 000130437 0247_ $$2doi$$a10.1016/j.jnt.2018.07.003 000130437 0248_ $$2sideral$$a107560 000130437 037__ $$aART-2018-107560 000130437 041__ $$aeng 000130437 100__ $$0(orcid)0000-0001-8331-5160$$aAdell, J.A.$$uUniversidad de Zaragoza 000130437 245__ $$aA probabilistic generalization of the Stirling numbers of the second kind 000130437 260__ $$c2018 000130437 5060_ $$aAccess copy available to the general public$$fUnrestricted 000130437 5203_ $$aAssociated 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. 000130437 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000130437 590__ $$a0.684$$b2018 000130437 591__ $$aMATHEMATICS$$b181 / 313 = 0.578$$c2018$$dQ3$$eT2 000130437 592__ $$a0.837$$b2018 000130437 593__ $$aAlgebra and Number Theory$$c2018$$dQ1 000130437 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000130437 700__ $$0(orcid)0000-0001-6555-4432$$aLekuona, A.$$uUniversidad de Zaragoza 000130437 7102_ $$12007$$2265$$aUniversidad de Zaragoza$$bDpto. Métodos Estadísticos$$cÁrea Estadís. Investig. Opera. 000130437 773__ $$g194 (2018), 335-355$$pJ. number theory$$tJOURNAL OF NUMBER THEORY$$x0022-314X 000130437 8564_ $$s447456$$uhttps://zaguan.unizar.es/record/130437/files/texto_completo.pdf$$yPostprint 000130437 8564_ $$s1268008$$uhttps://zaguan.unizar.es/record/130437/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000130437 909CO $$ooai:zaguan.unizar.es:130437$$particulos$$pdriver 000130437 951__ $$a2024-01-25-15:10:33 000130437 980__ $$aARTICLE