2024/09/17 by Antonio J. Durán, Durán, Antonio J.
Mathematics · #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2409.11344
openalex publication_date 2024/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, generalized Bell polynomials (\Benϕ)n associated to a sequence of real numbers ϕ=(ϕi)i=1^∞ are introduced. Bell polynomials correspond to ϕi=0, i≥ 1. We prove that when ϕi≥ 0, i≥ 1: (a) the zeros of the generalized Bell polynomial \Benϕ are simple, real and non positive; (b) the zeros of \Ben+1ϕ interlace the zeros of \Benϕ; (c) the zeros are decreasing functions of the parameters ϕi. We find a hypergeometric representation for the generalized Bell polynomials. As a consequence, it is proved that the class of all generalized Bell polynomials is actually the same class as that of all Laguerre multiple polynomials of the first kind.