Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Notes on a family of inhomogeneous linear ordinary differential equations, Advances and Applications in Mathematical Sciences 17 (2018), no. 4, 361--368.
Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Notes on a family of inhomogeneous linear ordinary differential equations, Advances and Applications in Mathematical Sciences 17 (2018), no. 4, 361--368.
Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Notes on a family of inhomogeneous linear ordinary differential equations, Advances and Applications in Mathematical Sciences 17 (2018), no. 4, 361--368.
Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Notes on a family of inhomogeneous linear ordinary differential equations, Advances and Applications in Mathematical Sciences 17 (2018), no. 4, 361--368.
Abstract
In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and an inversion formula for the Stirling numbers of the first and second kinds, the authors establish meaningfully and significantly two identities which simplify coefficients in a family of ordinary differential equations associated with higher order Bernoulli numbers of the second kind.
Keywords
simplification; coefficient; ordinary differential equation; higher order Bernoulli number of the second kind; Stirling number of the first kind; Stirling number of the second kind; inversion formula; Bell polynomial of the second kind; Faà di Bruno 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's Conflict of Interests:
I am the first and corresponding author
Comment:
This preprint has been formally publication as follows:
Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind, AIMS Mathematics 4 (2019), no. 2, 170--175; Available online at https://doi.org/10.3934/Math.2019.2.170
(Click to see Publons profile: )
Commenter's Conflict of Interests:
I am the first and corresponding author
Comment:
This preprint has been formally published as follows:
Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind, AIMS Mathematics 4 (2019), no. 2, 170--175; Available online at https://doi.org/10.3934/Math.2019.2.170
Commenter:
Commenter's Conflict of Interests: I am the first and corresponding author
Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind, AIMS Mathematics 4 (2019), no. 2, 170--175; Available online at https://doi.org/10.3934/Math.2019.2.170
Commenter:
Commenter's Conflict of Interests: I am the first and corresponding author
Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind, AIMS Mathematics 4 (2019), no. 2, 170--175; Available online at https://doi.org/10.3934/Math.2019.2.170