Extended stirling polynomials of the second kind and extended Bell polynomials
Taekyun Kim, Dae san Kim
TL;DR
This paper introduces extended Stirling and Bell polynomials, exploring their properties and expressing Bell polynomials in terms of Poisson distribution moments, thus expanding the mathematical framework of these combinatorial polynomials.
Contribution
It defines and analyzes extended Stirling and Bell polynomials, providing new expressions and connections to probability theory not previously established.
Findings
Extended Bell polynomials expressed via Poisson moments
New properties of extended Stirling polynomials derived
Enhanced understanding of combinatorial polynomial relationships
Abstract
Recently, several authors have studied the Stirling numbers of the second kind and Bell polynomials. In this paper, we study the extended Stirling polynomials of the second kind and the extended Bell polynomials associated with the Stirling numbers of the second kind. In addition, we note that the extended Bell polynomials can be expressed in terms of the moments of the Poisson random variable with parameter
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Mathematical functions and polynomials