Preprint Article Version 1 NOT YET PEER-REVIEWED

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

Feng Qi 1,2,3,* and Jiao-Lian Zhao 4
  1. Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China
  2. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region 028043, China
  3. Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City 300387, China
  4. Department of Mathematics and Informatics, Weinan Normal University, Weinan City, Shaanxi Province 714000, China
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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