Winding Numbers, Unwinding Numbers, and the Lambert W Function
Authors
Beardon, AF
Publication Date
2022-03Journal Title
Computational Methods and Function Theory
ISSN
1617-9447
Publisher
Springer Science and Business Media LLC
Volume
22
Issue
1
Pages
115-122
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Beardon, A. (2022). Winding Numbers, Unwinding Numbers, and the Lambert W Function. Computational Methods and Function Theory, 22 (1), 115-122. https://doi.org/10.1007/s40315-021-00398-1
Abstract
<jats:title>Abstract</jats:title><jats:p>The unwinding number of a complex number was introduced to process automatic computations involving complex numbers and multi-valued complex functions, and has been successfully applied to computations involving branches of the Lambert <jats:italic>W</jats:italic> function. In this partly expository note we discuss the unwinding number from a purely topological perspective, and link it to the classical winding number of a curve in the complex plane. We also use the unwinding number to give a representation of the branches <jats:inline-formula><jats:alternatives><jats:tex-math>$$W_k$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:math></jats:alternatives></jats:inline-formula> of the Lambert <jats:italic>W</jats:italic> function as a line integral.</jats:p>
Keywords
Article, Unwinding number, Winding number, Lambert W function, 33E99
Identifiers
s40315-021-00398-1, 398
External DOI: https://doi.org/10.1007/s40315-021-00398-1
This record's URL: https://www.repository.cam.ac.uk/handle/1810/335592
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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