Theorems · Theorem · complex analysis
DifferentiableOn.analyticOnNhd
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {s : Set ℂ} {f : ℂ → E},
DifferentiableOn ℂ f s → IsOpen s → AnalyticOnNhd ℂ f s- Defined in
- Mathlib.Analysis.Complex.CauchyIntegral
- Cited by
- 21 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.
Cites10
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
- 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
- IsOpen.mem_nhdsproof · cited by 470
- DifferentiableOnstatement and proof · cited by 419
- AnalyticOnNhdstatement · cited by 206
- DifferentiableOn.analyticAtproof · cited by 6
Cited by21
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4
- ProbabilityTheory.analyticOnNhd_complexMGFproof · cited by 3
- PeriodPair.analyticOnNhd_weierstrassPExceptproof · cited by 3
- DifferentiableOn.derivproof · cited by 3
- Complex.Gamma_mul_Gamma_add_halfproof · cited by 2
- UpperHalfPlane.eq_zero_of_frequentlyproof · cited by 2
- UpperHalfPlane.contMDiff_denom_zpowproof · cited by 2
- LSeries_analyticOnNhdproof · cited by 1
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_univ_re_eqproof · cited by 1
- analyticOn_riemannZetaproof · cited by 1
- DiffContOnCl.ball_subset_image_closedBallproof · cited by 1
- ZMod.completedLFunction_one_sub_evenproof · cited by 1