TL;DR
This paper surveys a family of polynomials, including De Moivre and Bell polynomials, highlighting their applications in power series, generating functions, and asymptotic expansions, and discusses historical contributions.
Contribution
It provides a comprehensive overview of these polynomials, their properties, and their historical development, emphasizing their utility in mathematical analysis.
Findings
Illustrates applications in formal power series
Demonstrates use in generating functions
Explores asymptotic expansion techniques
Abstract
We survey a family of polynomials that are very useful in all kinds of power series manipulations, and appearing more frequently in the literature. Applications to formal power series, generating functions and asymptotic expansions are described, and we discuss the related work of De Moivre, Arbogast and Bell.
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Taxonomy
TopicsAdvanced Mathematical Identities