LambertW

Lambert W function with complex domain and range. LambertW( z, k ) returns the kth branch of the function W defined by the equation W(z) * exp(z) = z. The complex value is obtained using Halley's method as described by Corless et al [1996], Adv. Comp. Math 5:329. The nominal precision is 1.E-13 but convergence can be poor very close to discontinuities, e.g. branch points.