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

Feng Qi; Da-Wei Niu; Bai-Ni Guo

doi:10.2478/tmmp-2018-0022

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

Tatra Mountains Mathematical Publications

Volume 72 (2018): Issue 1 (December 2018)

By: Feng Qi, Da-Wei Niu and Bai-Ni Guo

Open Access

|Mar 2019

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2018-0022 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 67 - 76

Submitted on: Jul 9, 2018

Published on: Mar 12, 2019

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

simplification,

coefficient,

ordinary differential equation,

Faà di Bruno formula,

higher order Frobenius–Euler number,

Bell polynomial of the second kind,

inversion formula

Related subjects:

Mathematics,

General mathematics

© 2019 Feng Qi, Da-Wei Niu, Bai-Ni Guo, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 72 (2018): Issue 1 (December 2018)