On the generalization of the Lambert 𝑊 function

Mező, István; Baricz, Árpád

doi:10.1090/tran/6911

On the generalization of the Lambert $W$ function
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by István Mező and Árpád Baricz PDF

Trans. Amer. Math. Soc. 369 (2017), 7917-7934 Request permission

Abstract:

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.

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