Series Transformations to Improve and Extend Convergence

We consider a new invariant transformation of some previously known series for the Lambert W function. The transformations contain a parameter p which can be varied, while retaining the basic series structure. The parameter can be used to expand the domain of convergence of the series. The speed of convergence, that is the accuracy for a given number of terms, can increase or decrease with p. Theoretical and experimental investigations that rely heavily on the computer-algebra system MAPLE are described.