Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
Holomorphic functions
Simply connected domains |
| gptkbp:category |
Theorems in analysis
|
| gptkbp:field |
Complex analysis
|
| gptkbp:generalizes |
Cauchy's theorem for multiply connected domains
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cauchy's integral theorem
|
| gptkbp:implies |
gptkb:Cauchy's_integral_formula
gptkb:Morera's_theorem |
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:publishedIn |
gptkb:Cauchy's_1825_paper
|
| gptkbp:relatedTo |
gptkb:Green's_theorem
Residue theorem |
| gptkbp:state |
If a function is holomorphic throughout a simply connected domain, then the integral of the function over any closed curve in the domain is zero.
|
| gptkbp:usedIn |
Proofs in complex analysis
|
| gptkbp:bfsParent |
gptkb:Cauchy–Goursat_theorem
gptkb:Cauchy_residue_theorem gptkb:Komplexe_Analysis |
| gptkbp:bfsLayer |
6
|