Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some properties and an application of multivariate exponential polynomials, Mathematical Methods in the Applied Sciences (2020), no.~6, 2967-2983; available online at https://doi.org/10.1002/mma.6095.
Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some properties and an application of multivariate exponential polynomials, Mathematical Methods in the Applied Sciences (2020), no.~6, 2967-2983; available online at https://doi.org/10.1002/mma.6095.
Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some properties and an application of multivariate exponential polynomials, Mathematical Methods in the Applied Sciences (2020), no.~6, 2967-2983; available online at https://doi.org/10.1002/mma.6095.
Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some properties and an application of multivariate exponential polynomials, Mathematical Methods in the Applied Sciences (2020), no.~6, 2967-2983; available online at https://doi.org/10.1002/mma.6095.
Abstract
In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.
Keywords
Bell number; Bell polynomial; generalization; explicit formula; inversion formula; inversion theorem; Stirling number; Bell polynomial of the second kind; determinantal inequality; product inequality; completely monotonic function; logarithmic convexity
Subject
Computer Science and Mathematics, Algebra and 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.
Received:
31 August 2017
Commenter:
Feng Qi
Commenter's Conflict of Interests:
I am the first and corresponding author of this preprint.
Comment:
Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, A unified generalization of the Bell numbers and the Touchard polynomials and its properties, ResearchGate Working Paper (2017), available online at https://doi.org/10.13140/RG.2.2.36733.05603
Received:
11 June 2018
Commenter:
Fng Qi
Commenter's Conflict of Interests:
I am the first and corresponding author of this preprint.
Comment:
This preprint is the original version of the following preprint:
Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some properties and an application of multivariate exponential polynomials, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01745173
(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
Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some properties and an application of multivariate exponential polynomials, Mathematical Methods in the Applied Sciences 43 (2020), no. 6, 2967--2983; available online at doi.org/10.1002/mma.6095https://doi.org/10.1002/mma.6095.
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author of this preprint.
Commenter: Fng Qi
Commenter's Conflict of Interests: I am the first and corresponding author of this preprint.
Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some properties and an application of multivariate exponential polynomials, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01745173
Commenter:
Commenter's Conflict of Interests: I am the first and corresponding author
Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some properties and an application of multivariate exponential polynomials, Mathematical Methods in the Applied Sciences 43 (2020), no. 6, 2967--2983; available online at doi.org/10.1002/mma.6095https://doi.org/10.1002/mma.6095.