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.
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.
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.
Keywords
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
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.
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.
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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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
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author for this preprint
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.
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author for this preprint
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
Commenter:
Commenter's Conflict of Interests: I am the first and corresponding author
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