Preprint Article Version 1 This version is not peer-reviewed

Some Identities Relating to Eulerian Polynomials and Involving Stirling Numbers

Version 1 : Received: 31 July 2017 / Approved: 2 August 2017 / Online: 2 August 2017 (17:03:00 CEST)

A peer-reviewed article of this Preprint also exists.

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

Journal reference: Applicable Analysis and Discrete Mathematics 2018, 12, 1-14
DOI: 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.

Subject Areas

identity; generating function; Eulerian polynomial; higher order Eulerian polynomial; Stirling number; open problem

Readers' Comments and Ratings (1)

Comment 1
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
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