A probabilistic generalization of the Stirling numbers of the second kind
Number Theory
2018-03-14 v1
Abstract
Associated to each random variable having a finite moment generating function, 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 in each case, are discussed in detail.
Keywords
Cite
@article{arxiv.1803.04914,
title = {A probabilistic generalization of the Stirling numbers of the second kind},
author = {José A. Adell and Alberto Lekuona},
journal= {arXiv preprint arXiv:1803.04914},
year = {2018}
}