Theorems · Theorem · complex analysis
Complex.cderiv_eq_deriv
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {U : Set ℂ} {z : ℂ} {r : ℝ} {f : ℂ → E}
[CompleteSpace E],
IsOpen U → DifferentiableOn ℂ f U → 0 < r → Metric.closedBall z r ⊆ U → Complex.cderiv r f z = deriv f z- Cited by
- 2 results in Mathlib
- Foundations
- Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- 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
- IsOpenstatement and proof · cited by 2,400
- Metric.closedBallstatement and proof · cited by 704
- derivstatement · cited by 676
- DifferentiableOnstatement and proof · cited by 419
- Metric.mem_ball_selfproof · cited by 40
- Complex.cderivstatement · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- TendstoLocallyUniformlyOn.derivproof · cited by 3
- Complex.tendstoUniformlyOn_deriv_of_cthickening_subsetproof · cited by 1