# The Boson normal ordering problem and generalized Bell numbers

Blasiak, P.; Penson, K.A. and Solomon, A.I. (2003). The Boson normal ordering problem and generalized Bell numbers. Annals of Combinatorics, 7(2) pp. 127–139.

## Abstract

For any function F(x) having a Taylor expansion we solve the boson normal ordering problem for , with r, s positive integers, , i.e., we provide exact and explicit expressions for its normal form = , where in all a's are to the right. The solution involves integer sequences of numbers which, for , are generalizations of the conventional Bell and Stirling numbers whose values they assume for . A complete theory of such generalized combinatorial numbers is given including closed-form expressions (extended Dobinski-type formulas), recursion relations and generating functions. These last are special expectation values in boson coherent states.

Item Type: Journal Article 2003 Birkhauser-Verlag 0219-3094 Some of the symbols may not have transferred correctly into this bibliographic record. boson normal order; Bell numbers; Stirling numbers; coherent states Science > Physical SciencesScience 4891 Users 6041 not found. 11 Aug 2006 14 Jan 2016 16:10 http://oro.open.ac.uk/id/eprint/4891

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