xexp {LambertW}

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)