ABSTRACT
The first chapter introduces the Lambert W function through the transcen- dental equation xex = a. It is shown that the W function solves not only this equation but many others, too, where exponentials of arbitrary base or loga- rithms appear. It is also shown in this chapter that there are several interesting functional equations that the Lambert function satisfies. The basic real analytic properties (derivatives, integrals, integral representations, Mellin and Laplace transform, etc.) of W are also studied.
In the last part, the Ω = W 0(1) special value is investigated.
