Cauchy Integral Formula
Evaluate a polynomial contour integral by its interior value or derivative and distinguish inside, outside and on-contour poles.
Free theory articleEvaluate a polynomial contour integral by its interior value or derivative and distinguish inside, outside and on-contour poles.
Concept & interpretation
The Cauchy Integral Formula is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk.
Experiment
Use the interactive visualization to explore different kernel points and contours:
- Set Analytic polynomial f to z^3.
- Set Kernel point a to 1.
- Set Contour radius R to 2.
- Set Derivative order m to 1.
- Observe that the status is Inside and the normalized_integral is 3.
See the interactive module at https://riano.app/module/cauchy-integral-formula.