Preprint Article Version 1 This version is not peer-reviewed

Some Properties of a Solution to a Family of Inhomogeneous Linear Ordinary Differential Equations

Version 1 : Received: 29 November 2016 / Approved: 29 November 2016 / Online: 29 November 2016 (08:00:53 CET)

A peer-reviewed article of this Preprint also exists.

Feng Qi and Bai-Ni Guo, A diagonal recurrence relation for the Stirling numbers of the first kind, Applicable Analysis and Discrete Mathematics 12 (2018), no. 1, 153--165; Available online at https://doi.org/10.2298/AADM170405004Q. Feng Qi and Bai-Ni Guo, A diagonal recurrence relation for the Stirling numbers of the first kind, Applicable Analysis and Discrete Mathematics 12 (2018), no. 1, 153--165; Available online at https://doi.org/10.2298/AADM170405004Q.

Journal reference: Applicable Analysis and Discrete Mathematics 2018, 12, 153-165
DOI: 10.2298/AADM170405004Q

Abstract

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

Subject Areas

explicit form; inhomogeneous linear ordinary differential equation; derivative; Lerch transcendent; absolute monotonicity; complete monotonicity; Bernstein function; inequality; diagonal recurrence relation; Stirling numbers of the first kind; logarithmic function

Readers' Comments and Ratings (3)

Comment 1
Received: 1 October 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author for this preprint
Comment: A revised version of this preprint has been accepted by Applicable Analysis and Discrete Mathematics, please cite this paper temporarily as

Feng Qi and Bai-Ni Guo, A diagonal recurrence relation for the Stirling numbers of the first kind, Applicable Analysis and Discrete Mathematics 12 (2018), in press.
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Comment 2
Received: 10 November 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author for this preprint
Comment: This preprint has been formally published online at https://doi.org/10.2298/AADM170405004Q

Feng Qi and Bai-Ni Guo, A diagonal recurrence relation for the Stirling numbers of the first kind, Applicable Analysis and Discrete Mathematics 12 (2018), in press; Available online at https://doi.org/10.2298/AADM170405004Q
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Comment 3
Received: 20 April 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author
Comment: This preprint has been formally published as

Feng Qi and Bai-Ni Guo, A diagonal recurrence relation for the Stirling numbers of the first kind, Applicable Analysis and Discrete Mathematics 12 (2018), no. 1, 153--165; Available online at https://doi.org/10.2298/AADM170405004Q
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