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On the generalization of the Lambert $ W$ function

Authors: István Mező and Árpád Baricz
Journal: Trans. Amer. Math. Soc. 369 (2017), 7917-7934
MSC (2010): Primary 33E99
Published electronically: April 13, 2017
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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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Additional Information

István Mező
Affiliation: Department of Mathematics, Nanjing University of Information Science and Technology, No. 219 Ningliu Rd, Nanjing, Jiangsu, People’s Republic of China

Árpád Baricz
Affiliation: Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary – and – Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania

Keywords: Lambert $W$ function, Stirling numbers, Laguerre polynomials, transcendence
Received by editor(s): April 13, 2015
Received by editor(s) in revised form: December 9, 2015
Published electronically: April 13, 2017
Additional Notes: The research of the first author was supported by the Scientific Research Foundation of Nanjing University of Information Science & Technology, the Startup Foundation for Introducing Talent of NUIST, Project no. S8113062001, and the National Natural Science Foundation for China, Grant no. 11501299.
The work of the second author was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
Article copyright: © Copyright 2017 American Mathematical Society

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