R: Transformation that defines the Lambert W function and its...

xexp {LambertW} | R Documentation

## Transformation that defines the Lambert W function and its derivative

### Description

The Lambert W function W(z) is the inverse of u \exp(u) = z.

In versions < 0.6.0 of the package this function was denoted as `H`. It is now replaced with the more descriptive `xexp` (and `H` is deprecated).

### Usage

    xexp(x)

    deriv_xexp(x, degree = 1)

### Arguments

`x` | a numeric vector of real/complex values.
`degree` | non-negative integer; degree of the derivative

### Details

The n-th derviative of x \cdot \exp(x) is available in closed for as

\exp(x) \cdot (x + n).

### Value

Returns z = x \exp(x) for x \in C. If x is a vector/matrix, so is z.

### See Also

`W`

### Examples

    plot(xexp, -5, 0.5, type="l", xlab="u", ylab="z")
    grid()
    abline(h=0, lty = 2)
    abline(v=0, lty = 2)

[Package LambertW version 0.6.7 Index]