Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials

Abstract

In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.

Keywords

• Faà di Bruno formula
• generalized Eulerian polynomial
• Bell polynomial of the second kind
• general formula for derivatives of the ratio between two differentiable functions
• explicit formula
• determinantal formula