Penson, K. A.; Blasiak, P.; Duchamp, G.; Horzela, A. and Solomon, A. I.
|DOI (Digital Object Identifier) Link:||http://dx.doi.org/10.1088/0305-4470/37/10/011|
|Google Scholar:||Look up in Google Scholar|
We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a, a†] = 1) monomials of the form exp[λ(a†)ra], r = 1, 2, ..., under the composition of their exponential generating functions. They turn out to be of Sheffer type. We demonstrate that two key properties of these sequences remain preserved under substitutional composition: (a) the property of being the solution of the Stieltjes moment problem; and (b) the representation of these sequences through infinite series (Dobiński-type relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobiński-type formulae and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.
|Item Type:||Journal Article|
|Copyright Holders:||2004 IOP Publishing Limited|
|Academic Unit/Department:||Science > Physical Sciences
|Depositing User:||Colin Smith|
|Date Deposited:||22 Dec 2009 10:34|
|Last Modified:||15 Jan 2016 12:14|
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