Bell numbers

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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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They even paid for Bell Number Three out of their own pockets - a kind of toll charge.
137] (the computations involve the Bell number which exhibits a superexponential growth).
Power and Associates recently ranked Cincinnati Bell number one in customer satisfaction for both local residential telephone service and residential long distance among mainstream users.
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.