The Bell Series of Integers
Returns the values of the Bell series.
bell(n)
n |
Vector of non-negative integers.
Values greater than 218 return an |
The Bell numbers emerge from a series expansion of exp(exp(x) - 1) for real x. The first few values are B_0 = 1, B_1 = 1, B_2 = 2, B_3 = 5, B_4 = 15. The series increases quickly so that overflow occurs when its argument is more than 218.
This function returns B_n.
T. W. Yee
Bell, E. T. (1934). Exponential polynomials. Ann. Math., 35, 258–277.
Bell, E. T. (1934). Exponential numbers. Amer. Math. Monthly, 41, 411–419.
## Not run: plot(0:10, bell(0:10), log = "y", type = "h", las = 1, col = "blue") ## End(Not run)
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