On the generalization of the Lambert $W$ function with applications in theoretical physics

摘要

The Lambert $W$ function, giving the solutions of a simple transcendentalequation, has become a famous function and arises in many applications incombinatorics, physics, or population dyamics just to mention a few. In thelast decade it turned out that some specific relativistic equations andmolecular physics problems need solutions of more general transcendentalequations. Thus a generalization of the Lambert function is necessary. In thispaper we construct this generalization which involves some special polynomials.