Dobinski-type relations: Some properties and physical applications

((1) Polish Academy of Sciences; (2) LPTL; 3); (3) The Open University; A Horzela (1); A I Solomon (2; France; K A Penson (2); Krakow; Milton Keynes

arxiv: quant-ph/0511157 · v1 · submitted 2005-11-16 · 🪐 quant-ph

Dobinski-type relations: Some properties and physical applications

P Blasiak (1) , A Horzela (1) , K A Penson (2) , A I Solomon (2 , 3) , ((1) Polish Academy of Sciences , Krakow , Poland

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(2) LPTL University of Paris VI France (3) The Open University Milton Keynes UK)

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classification 🪐 quant-ph

keywords extensionphysicalproblemrelationapplicationsbell-typebosoncontext

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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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Dobinski-type relations: Some properties and physical applications

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