Algebraic properties of the Lambert W Function from a result of Rosenlicht and of Liouville

Manuel Bronstein; Robert M Corless; James H Davenport; D J Jeffrey

doi:10.1080/10652460802332342

Algebraic properties of the Lambert W Function from a result of Rosenlicht and of Liouville

Manuel Bronstein, Robert M Corless, James H Davenport, D J Jeffrey

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Abstract

It is shown that the Lambert W function cannot be expressed in terms of the elementary, Liouvillian, functions. The proof is based on a theorem due to Rosenlicht. A related function, the Wright omega function is similarly shown to be not Liouvillian.

Original language	English
Pages (from-to)	709-712
Number of pages	4
Journal	Integral Transforms and Special Functions
Volume	19
Issue number	10
DOIs	https://doi.org/10.1080/10652460802332342
Publication status	Published - 2008

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Davenport_ITSF_19_10_709.pdf
This is an electronic version of an article published in Bronstein, M., Corless, R. M., Davenport, J. H. and Jeffrey, D.J., 2008. Algebraic properties of the Lambert W Function from a result of Rosenlicht and of Liouville. Integral Transforms and Special Functions, 19 (10), pp. 709-712. Integral Transforms and Special Functions is available online at http://dx.doi.org/10.1080/10652460802332342
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Cite this

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title = "Algebraic properties of the Lambert W Function from a result of Rosenlicht and of Liouville",

abstract = "It is shown that the Lambert W function cannot be expressed in terms of the elementary, Liouvillian, functions. The proof is based on a theorem due to Rosenlicht. A related function, the Wright omega function is similarly shown to be not Liouvillian.",

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AU - Davenport, James H

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AB - It is shown that the Lambert W function cannot be expressed in terms of the elementary, Liouvillian, functions. The proof is based on a theorem due to Rosenlicht. A related function, the Wright omega function is similarly shown to be not Liouvillian.

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Algebraic properties of the Lambert W Function from a result of Rosenlicht and of Liouville

Abstract

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