2004/12/02 by Elvira Di Nardo, E. Di Nardo, Di Nardo, E. +2
Mathematics · #05A40 #60C05 (Primary) 62A01(Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #math.CO #math.PR #msc:05A40 #msc:60C05
paper · pdf · doi:10.48550/arxiv.math/0412052
20 pages
arxiv created 2004/12/02 · openalex publication_date 2004/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide an algebraic setting for cumulants and factorial moments through the classical umbral calculus. Main tools are the compositional inverse of the unity umbra, connected with the logarithmic power series, and a new umbra here introduced, the singleton umbra. Various formulae are given expressing cumulants, factorial moments and central moments by umbral functions.