Dobinski-type relations: Some properties and physical applications
arXiv:quant-ph/0511157 · doi:10.1088/0305-4470/39/18/015
Abstract
We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the Kerr Hamiltonian.
7 pages, 1 figure