Preprint Article Version 1 This version is not peer-reviewed

Simplifying Coefficients in Differential Equations Associated with Higher Order Bernoulli Numbers of the Second Kind

Version 1 : Received: 5 August 2017 / Approved: 8 August 2017 / Online: 8 August 2017 (07:59:57 CEST)

A peer-reviewed article of this Preprint also exists.

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.

Journal reference: Advances and Applications in Mathematical Sciences 2018, 17, 361-368
DOI: 10.20944/preprints201704.0026.v1

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.

Subject Areas

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.

Comments (2)

Comment 1
Received: 21 March 2019
Commenter: Feng Qi
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
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Comment 2
Received: 21 March 2019
Commenter: Feng Qi
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
+ Respond to this comment

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