Simplifying coefficients in a family of nonlinear ordinary differential equations

Authors

  • Feng Qi Institute of Mathematics, Henan Polytechnic University, Jiaozuo, Henan, 454010, China; College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia, 028043, China; Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, 300387, China

DOI:

https://doi.org/10.12697/ACUTM.2018.22.24

Keywords:

simplifying, coefficient, nonlinear ordinary differential equation, Faá di Bruno formula, Stirling number, Bell polynomials of the second kind, binomial inversion formula, Lah number

Abstract

By virtue of the Faá di Bruno formula, properties of the Stirling numbers and the Bell polynomials of the second kind, the binomial inversion formula, and other techniques in combinatorial analysis, the author finds a simple, meaningful, and signicant expression for coefficients in a family of nonlinear ordinary differential equations.

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Published

2019-01-02

Issue

Vol. 22 No. 2 (2018)

Section

Articles