Article
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Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
Version 1
: Received: 12 October 2016 / Approved: 12 October 2016 / Online: 12 October 2016 (11:47:48 CEST)
How to cite: Qi, F.; Guo, B. Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials. Preprints 2016, 2016100043 (doi: 10.20944/preprints201610.0043.v1). Qi, F.; Guo, B. Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials. Preprints 2016, 2016100043 (doi: 10.20944/preprints201610.0043.v1).
Abstract
In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.
Keywords
viewpoint; ordinary differential equation; solution; derivative polynomial; identity; Stirling numbers; Bernoulli number; Bernoulli polynomial; Frobenius-Euler polynomial
Subject
MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory
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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Bai-Ni Guo and Feng Qi, \textit{Viewing some ordinary differential equations from the angle of derivative polynomials}, Iranian Journal of Mathematical Sciences and Informatics \textbf{16} (2021), no.~1, 77\nobreakdash--95; available online at \url{https://doi.org/10.29252/ijmsi.16.1.77