Article
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Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius–Euler Numbers
Version 1
: Received: 4 August 2017 / Approved: 4 August 2017 / Online: 4 August 2017 (15:47:44 CEST)
A peer-reviewed article of this Preprint also exists.
Abstract
In the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.
Keywords
simplification; coefficient; ordinary differential equation; higher order Frobenius–Euler number; Fa`a di Bruno formula; Bell polynomial of the second kind; inversion formula
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter:
Commenter's Conflict of Interests: I am the first and corresponding author
Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplification of coefficients in differential equations associated with higher order FrobeniusEuler numbers, Tatra Mountains Mathematical Publications 72 (2018), 6776; Available online at https://doi.org/10.2478/tmmp-2018-0022
Commenter:
Commenter's Conflict of Interests: I am the first and corresponding author
Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplification of coefficients in differential equations associated with higher order Frobenius—Euler numbers, Tatra Mountains Mathematical Publications 72 (2018), 67—76; available online at https://doi.org/10.2478/tmmp-2018-0022