Herein, we use Hardy's notion of the "false derivative" to obtain exact multiple roots in closed form of the transcendental-algebraic equations representing the generalized Lambert  W  function. In this fashion, we flesh out the generalized Lambert  W  function by complementing previous developments to produce a more complete and integrated body of work. Finally, we demonstrate the usefulness of this special function with some applications.
['Aude Maignan', 'Tony Scott']
Fleshing out the generalized Lambert W function