Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
analytic functions
|
| gptkbp:discoveredIn |
1825
|
| gptkbp:field |
Complex analysis
|
| gptkbp:generalizes |
gptkb:Cauchy's_differentiation_formula
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cauchy's integral formula
|
| gptkbp:implies |
analytic functions are infinitely differentiable
|
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:publishedIn |
Cauchy's works on complex analysis
|
| gptkbp:state |
If f is analytic inside and on a simple closed contour C, and a is inside C, then f(a) = (1/2πi) ∮_C f(z)/(z-a) dz
|
| gptkbp:usedFor |
evaluating integrals
proving Liouville's theorem proving Morera's theorem |
| gptkbp:bfsParent |
gptkb:Cauchy's_theorem
gptkb:Cauchy's_integral_theorem gptkb:residue_theorem gptkb:Complex_Analysis gptkb:Contour_integration |
| gptkbp:bfsLayer |
7
|