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|
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We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form exp(x (a*)^r a), r=1,2,..., under the composition of their exponential generating functions (egf). 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 (Dobinski-type relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobinski-type formulas and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.
|Item Type:||Journal Article|
|Academic Unit/Department:||Science > Physical Sciences
|Depositing User:||Users 6042 not found.|
|Date Deposited:||13 Jul 2006|
|Last Modified:||14 Jan 2016 16:09|
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