### Abstract

In complex analysis, the winding number measures the number of times a path (counterclockwise) winds around a point, while the Cauchy index can approximate how the path winds. This entry provides a formalisation of the Cauchy index, which is then shown to be related to the winding number. In addition, this entry also offers a tactic that enables users to evaluate the winding number by calculating Cauchy indices.

### License

BSD License

### Topics

- Mathematics/Analysis

### Session Winding_Number_Eval

- Missing_Topology
- Missing_Algebraic
- Missing_Transcendental
- Missing_Analysis
- Cauchy_Index_Theorem
- Winding_Number_Eval
- Winding_Number_Eval_Examples

### Depends on

- The Budan–Fourier Theorem and Counting Real Roots with Multiplicity
- The Sturm–Tarski Theorem

### Used by

- Count the Number of Complex Roots
- The Hurwitz and Riemann ζ Functions

### Auto-related entries

- Wetzel’s Problem and the Continuum Hypothesis

## Cite

×

Winding_Number_Eval-AFP

    @article{Winding_Number_Eval-AFP,
      author  = {Wenda Li},
      title   = {Evaluate Winding Numbers through Cauchy Indices},
      journal = {Archive of Formal Proofs},
      month   = {October},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/Winding_Number_Eval.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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