Eulerian polynomials via the Weyl algebra action
Eulerian polynomials via the Weyl algebra action
Abstract Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family of polynomials including the classical Eulerian polynomials. We obtain an extension of the Dobiński formula for the sum of rook numbers of a …