# Normally ordered forms of powers of differential operators and their combinatorics

#### Preprint

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.

Emmanuel Briand

Mercedes Rosas

### Publication

Year of publication: 2018