Hierarchical Dobinski-type relations via substitution and the moment problem

Details Hierarchical Dobinski-type relations via substitution and the moment problem Hierarchical Dobinski-type relations via substitution and the moment problem

2003-12-26

arxiv.org/abs/quant-ph/0312202v1

J.Phys.A:Math.Gen.37 (2004)3475-3487

Physics

Quantum Physics

14 pages, 31 references

Scientific paper

10.1088/0305-4470/37/10/011

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.

Affiliated with

Also associated with

No associations

Rating

Hierarchical Dobinski-type relations via substitution and the moment problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hierarchical Dobinski-type relations via substitution and the moment problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hierarchical Dobinski-type relations via substitution and the moment problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-301187