Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
analytic functions
|
| gptkbp:category |
theorems in complex analysis
|
| gptkbp:field |
complex analysis
|
| gptkbp:firstPublished |
1825
|
| gptkbp:generalizes |
gptkb:Cauchy's_integral_theorem
Cauchy integral formula for derivatives |
| gptkbp:hasDerivativeForm |
f^{(n)}(a) = n!/(2πi) ∮_C f(z)/(z-a)^{n+1} dz
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cauchy integral formula
|
| gptkbp:implies |
analytic functions are infinitely differentiable
|
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:sentence |
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
|
| gptkbp:usedIn |
gptkb:Laurent_series
gptkb:residue_theorem contour integration |
| gptkbp:bfsParent |
gptkb:Bochner–Martinelli_formula
gptkb:Cauchy_integral_theorem |
| gptkbp:bfsLayer |
6
|