Journal
COMPUTATIONAL METHODS AND FUNCTION THEORY
Volume 22, Issue 1, Pages 115-122Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40315-021-00398-1
Keywords
Unwinding number; Winding number; Lambert W function
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The unwinding number of a complex number is used for automatic computations involving complex numbers and multi-valued complex functions, and has been successfully applied to computations involving branches of the Lambert W function. By discussing the unwinding number from a purely topological perspective and linking it to the classical winding number of a curve in the complex plane, we are able to represent the branches Wk of the Lambert W function as a line integral.
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 W function. In this partly expository notewe 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 Wk of the Lambert W function as a line integral.
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