Normally ordered forms of powers of differential operators and their combinatorics

Emmanuel Briand; Samuel A. Lopes; Mercedes Rosas

doi:10.1016/j.jpaa.2020.106312

paper

Normally ordered forms of powers of differential operators and their combinatorics

arXiv:1811.00857 · doi:10.1016/j.jpaa.2020.106312

Abstract

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.

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