bell: The Bell Series of Integers

In VGAM: Vector Generalized Linear and Additive Models

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.

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.

Value

This function returns B_{n}.

Author(s)

T. W. Yee

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: 
plot(0:10, bell(0:10), log = "y", type = "h", col = "blue")

## End(Not run)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.