H {LambertW}R Documentation

Orginal function defining the Lambert W function

Description

The Lambert W function W(z) is the inverse of this function: H(u) = u exp(u) = z.

Usage

H(u)

Arguments

u a numeric vector of real/complex values.

Value

Returns z = u exp(u) for u in C. If u is a vector, so is z.

Author(s)

Georg M. Goerg

References

Goerg, G.M. (2009). “Lambert W Random Variables - A new class of skewed distribution functions”. Unpublished

Examples

H(0)
W(0)

H(10)
W(H(10))

## at the critical point z = -1, both branches give the same inverse.
H(-1)
W(H(-1))
W_1(H(-1))

## going further to the left, the principal branch gives the 'wrong' solution; 
## the non-principal must be used
H(-10)
W(H(-10))
W_1(H(-10))

[Package LambertW version 0.1.9 Index]