Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
analytic functions
|
| gptkbp:category |
theorems in complex analysis
|
| gptkbp:field |
complex analysis
|
| gptkbp:generalizes |
gptkb:Cauchy's_residue_theorem
gptkb:Cauchy's_integral_theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Cauchy's theorem
|
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:publishedIn |
gptkb:Cauchy's_1825_paper
|
| gptkbp:relatedTo |
gptkb:Cauchy's_integral_formula
gptkb:Cauchy's_residue_theorem |
| gptkbp:sentence |
If a function is analytic and the domain is simply connected, then the integral of the function over any closed curve in the domain is zero.
|
| gptkbp:usedIn |
proofs in complex analysis
complex integration contour integration |
| gptkbp:bfsParent |
gptkb:Sylow_theorems
gptkb:Lagrange's_theorem |
| gptkbp:bfsLayer |
6
|