The Ubiquitous Lambert Function and its Classes in Sciences and Engineering

Christina Katsimpiri (), Panayotis E. Nastou (), Panos M. Pardalos () and Yannis C. Stamatiou ()
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Christina Katsimpiri: University of Aegean, Department of Mathematics
Panayotis E. Nastou: University of Aegean, Department of Mathematics
Panos M. Pardalos: University of Florida, Center for Applied Optimization
Yannis C. Stamatiou: University of Patras, Department of Business Administration

A chapter in Contributions in Mathematics and Engineering, 2016, pp 323-342 from Springer

Abstract: Abstract The Lambert-W function satisfies the functional equation W(x)e W(x) = x. This function shares with many other functions the remarkable property of appearing frequently in the solutions of a variety of mathematical problems stemming from diverse scientific domains that range from chemistry and mechanical engineering to computer science and network design. In this paper we survey some recent research results on various, diverse problems whose solutions involve the Lambert-W function as well as a natural extension there of, called Hyper Lambert functions. Our approach relies on highlighting the intuition behind the appearance of the Lambert function in the solution to these problems rather than providing fine details of the solution process, which can be found in the original research works. Our hope is that our work will be useful to other researchers working in similar problems serving as a guideline for uncovering a solution to their research problem that possibly involves the Lambert-W function or it extensions.

Keywords: Channel State Information; Relay Station; Wireless Mesh Network; Relay Network; Resource Allocation Problem (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31317-7_16

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DOI: 10.1007/978-3-319-31317-7_16

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