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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).
H
xexp
xexp(x)deriv_xexp(x, degree = 1)
deriv_xexp(x, degree = 1)
Returns \(z = x \exp(x)\) for \(x \in C\). If \(x\) is a vector/matrix, so is \(z\).
a numeric vector of real/complex values.
non-negative integer; degree of the derivative
The n-th derviative of \(x \cdot \exp(x)\) is available in closed for as
$$ \exp(x) \cdot (x + n).$$
W
plot(xexp, -5, 0.5, type="l", xlab="u", ylab="z") grid() abline(h=0, lty = 2) abline(v=0, lty = 2)
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