Some identities of Eulerian polynomials arising from nonlinear differential equations

TL;DR

This paper explores nonlinear differential equations related to Eulerian polynomials, deriving new identities and revealing their applications in mathematical analysis.

Contribution

It introduces novel identities involving Eulerian and higher-order Eulerian polynomials derived from nonlinear differential equations.

Findings

New explicit identities for Eulerian polynomials

Applications of these identities in mathematical analysis

Enhanced understanding of nonlinear differential equations related to Eulerian polynomials

Abstract

In this paper, we study nonlinear differential equations arising from Eulerian polynomials and their applications. From our study of nonlinear differential equations, we derive some new and explicit identities involving Eulerian and higher-order Eulerian polynomials.