Determinantal expressions and recurrence relations for Fubini and Eulerian polynomials

Abstract

In the paper, by virtue of an explicit formula for higher order derivatives of the ratio between two differentiable functions in terms of the Hessenberg determinant, the author presents determinantal expressions and recurrence relations for generalized Fubini polynomials. Hereafter, by virtue of relations between Eulerian polynomials and the (generalized) Fubini numbers and polynomials, the author derives a determinantal expression for Eulerian polynomials and several recurrence relations for the Fubini and Eulerian polynomials.

Subject Classification:

• (2010) Primary 11B68
• Secondary 11B37
• 11B83
• 26A24
• 26C05
• 33B10

Keywords:

• Generalized Fubini polynomial
• Eulerian polynomial
• Determinantal expression
• Recurrence relation
• Hessenberg determinant