On the generalization of the Lambert $W$ function

István Mező, Árpád Baricz
2017 Transactions of the American Mathematical Society  
The Lambert W function, giving the solutions of a simple transcendental equation, has become a famous function and arises in many applications in combinatorics, physics, or population dyamics just to mention a few. In this paper we construct and study in great detail a generalization of the Lambert W which involves some special polynomials and even combinatorial aspects.
doi:10.1090/tran/6911 fatcat:z6fxguaznfe45lj4tcwtoksgjq