Blasiak, P.; Penson, K.A. and Solomon, A.I.
(2003).
Dobinskitype relations and the lognormal distribution.
Journal of Physics A: Mathematical and General, 36(18) L273L278.
Abstract
We consider sequences of generalized Bell numbers B(n), n 1, 2, ..., which can be represented by Dobinskitype 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 lognormal distributions.
Item Type: 
Journal Article

ISSN: 
03054470 
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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