Preprint Article Version 1 NOT YET PEER-REVIEWED

The Bell Polynomials and a Sequence of Polynomials Applied to Differential Equations

Version 1 : Received: 29 November 2016 / Approved: 29 November 2016 / Online: 29 November 2016 (07:04:11 CET)

How to cite: Qi, F.; Zhao, J. The Bell Polynomials and a Sequence of Polynomials Applied to Differential Equations. Preprints 2016, 2016110147 (doi: 10.20944/preprints201611.0147.v1). Qi, F.; Zhao, J. The Bell Polynomials and a Sequence of Polynomials Applied to Differential Equations. Preprints 2016, 2016110147 (doi: 10.20944/preprints201611.0147.v1).

Abstract

In the paper, the authors discuss the Bell polynomials and a sequence of polynomials applied to the theory of hyperbolic differential equations. Concretely speaking, the authors find four explicit formulas for these polynomials and for derivatives of generating functions of these polynomials, establish four identities between these two kinds of polynomials, and significantly simplify some known results.

Subject Areas

Bell polynomial; explicit formula; derivative; Stirling number; generating function; identity; Faà di Bruno formula; differential equation

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