Function File: x = lambertw (z)

Function File: x = lambertw (z, n)

Compute the Lambert W function of z.

This function satisfies W(z).*exp(W(z)) = z, and can thus be used to express solutions of transcendental equations involving exponentials or logarithms.

n must be integer, and specifies the branch of W to be computed; W(z) is a shorthand for W(0,z), the principal branch. Branches 0 and -1 are the only ones that can take on non-complex values.

If either n or z are non-scalar, the function is mapped to each element; both may be non-scalar provided their dimensions agree.

This implementation should return values within 2.5*eps of its counterpart in Maple V, release 3 or later. Please report any discrepancies to the author, Nici Schraudolph <schraudo@inf.ethz.ch>.

For further details, see:

Corless, Gonnet, Hare, Jeffrey, and Knuth (1996), `On the Lambert W Function', Advances in Computational Mathematics 5(4):329-359.