LambertW (version 0.6.4)

xexp: 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

Value

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

Details

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

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

See Also

W

Examples

# NOT RUN {
plot(xexp, -5, 0.5, type="l", xlab="u", ylab="z")
grid()
abline(h=0, lty = 2)
abline(v=0, lty = 2)

# }