Dobinski-type relations: some properties and physical applications

Blasiak, P.; Horzela, A.; Penson, K. A. and Solomon, A. I. (2006). Dobinski-type relations: some properties and physical applications. Journal of Physics A: Mathematical and General, 39 pp. 4999–5006.

DOI: https://doi.org/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.

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