Bell numbers

Bell numbers

[′bel ‚nəm·bərz]
(mathematics)
The numbers, Bn , that count the total number of partitions of a set with n elements.
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Among their topics are basic tools, Stirling and Bell numbers, normal ordering in the Weyl algebra, a generalization of the Weyl algebra, and the q-deformed generalized Weyl algebra.
m](n) is known to be a generalization of the classical Bell numbers which is the sum of the Stirling numbers of the second kind S(n, k).
The following beautiful integral representation of the Bell numbers [B.
This expression was generalized by Mezo [11] using a kind of generalization of the classical Bell numbers called r-Bell numbers [B.
24] established the Hankel transform of the noncentral Bell numbers which is identical to that of the Bell and r-Bell case.
Note that when [alpha] = 1, we recover from (74) the Hankel transform of the classical Bell numbers of Aigner [19], the Hankel transform of the r-Bell numbers of Mezo [11], and the Hankel transform of the noncentral Bell numbers in [24].
Callan, "Cesaro's integral formula for the Bell numbers (corrected)," http://arxiv.
Aigner, "A characterization of the Bell numbers," Discrete Mathematics, vol.