VGAM (version 1.1-5)

bell: The Bell Series of Integers

Description

Returns the values of the Bell series.

Usage

bell(n)

Arguments

n

Vector of non-negative integers. Values greater than 218 return an Inf. Non-integers or negative values return a NaN.

Value

This function returns \(B_{n}\).

Details

The Bell numbers emerge from a series expansion of \( \exp(e^x - 1)\) 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.

References

Bell, E. T. (1934). Exponential polynomials. Ann. Math., 35, 258--277.

Bell, E. T. (1934). Exponential numbers. Amer. Math. Monthly, 41, 411--419.

See Also

bellff, rbell.

Examples

# NOT RUN {
 
# }
# NOT RUN {
plot(0:10, bell(0:10), log = "y", type = "h", las = 1, col = "blue")
# }