Blasiak, P.; Penson, K.A. and Solomon, A.I.
(2003).
Dobinski-type relations and the log-normal distribution.
Journal of Physics A: Mathematical and General, 36(18),
L273-L278.
Abstract
We consider sequences of generalized Bell numbers B(n), n 1, 2, ..., which can be represented by Dobinski-type summation formulae, i.e. B(n)1/Ck0[P(k)]n/D(k), with P(k) a polynomial, D(k) a function of k and C const. They include the standard Bell numbers (P(k) k, D(k) k!,Ce), their generalizations Br,r(n), r 2, 3, ..., appearing in the normal ordering of powers of boson monomials (P(k) (k+r)!/k!, D(k) k!, Ce), variants of 'ordered' Bell numbers Bo(p)(n) (P(k) k, D(k) (p+1/p)k, C 1 + p, p 1, 2 ...), etc. We demonstrate that for , , , t positive integers (, t 0), [B(n2 + n + )]t is the nth moment of a positive function on (0,) which is a weighted infinite sum of log-normal distributions.
| Item Type: |
Journal Article
|
| ISSN: |
0305-4470 |
| Extra Information: |
Some of the symbols may not have transferred correctly into this bibliographic record. |
| Academic Unit/Department: |
Science > Physical Sciences |
| Item ID: |
4889 |
| Depositing User: |
Users 6041 not found. |
| Date Deposited: |
11 Aug 2006 |
| Last Modified: |
02 Dec 2010 19:52 |
| URI: |
http://oro.open.ac.uk/id/eprint/4889 |
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