Theorems · Theorem · complex analysis
Differentiable.analyticAt
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E},
Differentiable ℂ f → ∀ (z : ℂ), AnalyticAt ℂ f zA complex differentiable function f : ℂ → E is analytic at every point.
- Defined in
- Mathlib.Analysis.Complex.CauchyIntegral
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- CompleteSpacestatement and proof · cited by 2,532
- AnalyticAtstatement · cited by 321
- Differentiablestatement and proof · cited by 298
- Filter.univ_memproof · cited by 96
- Differentiable.differentiableOnproof · cited by 40
- DifferentiableOn.analyticAtproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Differentiable.contDiffproof · cited by 3