Preprint Article Version 1 This version not peer reviewed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)

How to cite: Qi, F.; Lim, D.; Guo, B. Some Identities Relating to Eulerian Polynomials and Involving Stirling Numbers. Preprints 2017, 2017080004 (doi: 10.20944/preprints201708.0004.v1). Qi, F.; Lim, D.; Guo, B. Some Identities Relating to Eulerian Polynomials and Involving Stirling Numbers. Preprints 2017, 2017080004 (doi: 10.20944/preprints201708.0004.v1).

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

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