<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the paper, the authors apply Faà di Bruno formula, some properties of the Bell polynomials of the second kind, the inversion formulas of binomial numbers and the Stirling numbers of the first and the second kind, to significantly simplify coefficients in two families of ordinary differential equations associated with the higher order Frobenius–Euler numbers.</p></abstract>

In the paper, the authors apply Faà di Bruno formula, some properties of the Bell polynomials of the second kind, the inversion formulas of binomial numbers and the Stirling numbers of the first and the second kind, to significantly simplify coefficients in two families of ordinary differential equations associated with the higher order Frobenius–Euler numbers.

Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius-Euler Numbers

Inner Mongolia University for Nationalities

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In the paper, the authors apply Faà di Bruno formula, some properties of the Bell polynomials of the second kind, the inversion formulas of binomial numbers...

Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius-Euler Numbers

Published Online: Mar 12, 2019

Page range: 67 - 76

Received: Jul 09, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0022

Keywords
simplification, coefficient, ordinary differential equation, Faà di Bruno formula, higher order Frobenius–Euler number, Bell polynomial of the second kind, inversion formula

© 2018 Feng Qi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius-Euler Numbers

Published Online: Mar 12, 2019

Page range: 67 - 76

Received: Jul 09, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0022

Keywordssimplification, coefficient, ordinary differential equation, Faà di Bruno formula, higher order Frobenius–Euler number, Bell polynomial of the second kind, inversion formula

© 2018 Feng Qi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
simplification, coefficient, ordinary differential equation, Faà di Bruno formula, higher order Frobenius–Euler number, Bell polynomial of the second kind, inversion formula