Winding number
Intuitively, the winding number of a curve γ with respect to a point z0 is the number of times γ goes around z0 in a counter-clockwise direction.
Formally, the winding number is defined as follows:
If γ is a closed curve in C, and z0 is a point in C not on γ, then the winding number of γ with respect to z0 (alternately called the index of γ with respect to z0) is defined by the formula:
- I(γ, z0) = 1/(2πi) ∫γ 1/(z – z0) dz
The winding number is used primarily in complex analysis in the Residue theorem.
Referenced By
List of complex analysis topics | List of mathematical topics (V-Z)
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