VGAM (version 1.1-1)

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")
# }