On the Lambert \(w\) function
type: Item
instance of: scholarly article
title: On the Lambert \(w\) function
zbMATH Open document ID: 0863.65008
DOI: 10.1007/BF02124750
author: D. E. G. Hare
author: Robert M. Corless
author: Gaston H. Gonnet
author: D. J. Jeffrey
author: Donald E. Knuth
published in: Advances in Computational Mathematics
publication date: 1997-06-08T00:00:00Z
review text: The tree function \(T\) defined by series \(T(v)=v+{2\over 2!}v^2+{3^2\over 3!}v^3+{4^3\over 4!}v^4+\dots\) converges for \(|v|< {1\over e}\). It equals \(-w(-v)\), where \(w(z)\) is defined to be the function satisfying \(w(z)e^{w(z)}=z\). This paper discusses both \(w\) and \(T\), concentrating on \(w\). The authors present a new discussion of the complex branches for \(w\), an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containing \(w\).
reviewed by: R. S. Dahiya
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 65D20
zbMATH DE Number: 947614
zbMATH Keywords: Lambert \(w\) function
zbMATH Keywords: tree function
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: symbolic integration
Wikidata QID: Q55878644
describes a project that uses: Algorithm 443
describes a project that uses: Maple
describes a project that uses: LambertW
MaRDI profile type: Publication
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DBLP publication ID: journals/adcm/CorlessGHJK96
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description: scientific article; zbMATH DE number 947614