Asymptotic Limit and Bounds
Several asymptotic formulae for the Bell numbers are known. One such is
Here
where W is the Lambert W function. (Lovász, 1993)
Moser and Wyman established the expansion
uniformly for as, where and each and are known expressions in .
In (Berend, D. and Tassa, T., 2010), the following bounds were established:
moreover, if then for all ,
where and 
Read more about this topic: Bell Number
Famous quotes containing the words limit and/or bounds:
“We live in oppressive times. We have, as a nation, become our own thought police; but instead of calling the process by which we limit our expression of dissent and wonder “censorship,” we call it “concern for commercial viability.””
—David Mamet (b. 1947)
“Firmness yclept in heroes, kings and seamen,
That is, when they succeed; but greatly blamed
As obstinacy, both in men and women,
Whene’er their triumph pales, or star is tamed —
And ‘twill perplex the casuist in morality
To fix the due bounds of this dangerous quality.”
—George Gordon Noel Byron (1788–1824)