Hierarchical Dobinskitype relations via substitution and the moment problem
Abstract
We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a, adagger] = 1) monomials of the form exp[lgr(adagger)^{r}a], 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 (Dobinskitype relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobinskitype formulae and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2004
 DOI:
 10.1088/03054470/37/10/011
 arXiv:
 arXiv:quantph/0312202
 Bibcode:
 2004JPhA...37.3475P
 Keywords:

 Quantum Physics;
 Mathematics  Combinatorics
 EPrint:
 14 pages, 31 references