Powers of the operator $u(z)\frac{d}{dz}$ and their connection with some combinatorial numbers
Year: 2024
Type: article
Abstract: In this paper the operator $A = u(z)\frac{d}{dz}$ is considered, where $u$ is an entire or \linebreak meromorphic function in the complex plane. The expansion of $A^{k}$ ($k\geq1$) with the help of the powers of the differential operator $D=\frac{d}{dz}$ is obtained, and it is shown that this expansion depends on special numbers. Connections between these numbers and known combinatorial numbers are given. Some special cases of the operator $A$, corresponding to $u(z) = z, u(z) = e^{z}, u(z) = \frac{1}{z},$ are considered.
Author: Ioana Petkova
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Bulgarian National Science Fund
Award: G1907175571
OpenAlex ID: W4404180809