Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Some identities related to Eulerian polynomials and involving the Stirling numbers, Applicable Analysis and Discrete Mathematics 12 (2018), no. 2, in press; Available online at https://doi.org/10.2298/AADM171008014Q
Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Some identities related to Eulerian polynomials and involving the Stirling numbers, Applicable Analysis and Discrete Mathematics 12 (2018), no. 2, in press; Available online at https://doi.org/10.2298/AADM171008014Q
Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Some identities related to Eulerian polynomials and involving the Stirling numbers, Applicable Analysis and Discrete Mathematics 12 (2018), no. 2, in press; Available online at https://doi.org/10.2298/AADM171008014Q
Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Some identities related to Eulerian polynomials and involving the Stirling numbers, Applicable Analysis and Discrete Mathematics 12 (2018), no. 2, in press; Available online at https://doi.org/10.2298/AADM171008014Q
Abstract
In the paper, the authors establish two identities, which can be regarded as nonlinear differential equations, for the generating function of Eulerian polynomials, find two identities for the Stirling numbers of the second kind, and present two identities for Eulerian polynomials and higher order Eulerian polynomials, pose two open problems about summability of two finite sums involving the Stirling numbers of the second kind. Some of these conclusions meaningfully and significantly simplify several known results.
Keywords
identity; generating function; Eulerian polynomial; higher order Eulerian polynomial; Stirling number; open problem
Subject
Computer Science and Mathematics, Computational Mathematics
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:
26 July 2018
Commenter:
Feng Qi
Commenter's Conflict of Interests:
I am the first and corresponding author
Comment:
This preprint has been accepted and published, please cite it as follow
Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Some identities related to Eulerian polynomials and involving the Stirling numbers, Applicable Analysis and Discrete Mathematics 12 (2018), no. 2, in press; Available online at https://doi.org/10.2298/AADM171008014Q
(Click to see Publons profile: )
Commenter's Conflict of Interests:
I am the first and corresponding author
Comment:
Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Some identities related to Eulerian polynomials and involving the Stirling numbers, Applicable Analysis and Discrete Mathematics 12 (2018), no. 2, 467--480; Available online at https://doi.org/10.2298/AADM171008014Q
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author
Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Some identities related to Eulerian polynomials and involving the Stirling numbers, Applicable Analysis and Discrete Mathematics 12 (2018), no. 2, in press; Available online at https://doi.org/10.2298/AADM171008014Q
Commenter:
Commenter's Conflict of Interests: I am the first and corresponding author