dorsal/arxiv
View SchemaHierarchical Dobinski-type relations via substitution and the moment problem
| Authors | K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela, A. I. Solomon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312202 |
| URL | https://arxiv.org/abs/quant-ph/0312202 |
| DOI | 10.1088/0305-4470/37/10/011 |
| Journal | J.Phys.A:Math.Gen.37 (2004)3475-3487 |
Abstract
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.
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"abstract": "We consider the transformation properties of integer sequences arising from\nthe normal ordering of exponentiated boson ([a,a*]=1) monomials of the form\nexp(x (a*)^r a), r=1,2,..., under the composition of their exponential\ngenerating functions (egf). They turn out to be of Sheffer-type. We demonstrate\nthat two key properties of these sequences remain preserved under\nsubstitutional composition: (a)the property of being the solution of the\nStieltjes moment problem; and (b) the representation of these sequences through\ninfinite series (Dobinski-type relations). We present a number of examples of\nsuch composition satisfying properties (a) and (b). We obtain new Dobinski-type\nformulas and solve the associated moment problem for several hierarchically\ndefined combinatorial families of sequences.",
"arxiv_id": "quant-ph/0312202",
"authors": [
"K. A. Penson",
"P. Blasiak",
"G. Duchamp",
"A. Horzela",
"A. I. Solomon"
],
"categories": [
"quant-ph",
"math.CO"
],
"doi": "10.1088/0305-4470/37/10/011",
"journal_ref": "J.Phys.A:Math.Gen.37 (2004)3475-3487",
"title": "Hierarchical Dobinski-type relations via substitution and the moment problem",
"url": "https://arxiv.org/abs/quant-ph/0312202"
},
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