Normally ordered forms of powers of differential operators and their combinatorics

Emmanuel Briand, Samuel A. Lopes, Mercedes Rosas

Published 2018-11-02Version 1

We investigate the combinatorics of the general formulas for the powers of the operator $h \partial^k$, where $h$ is a central element of a ring and $\partial$ is a differential operator. This generalizes previous work on the powers of operators $h \partial$. New formulas for the generalized Stirling numbers are obtained.