Theorems · Theorem · complex analysis
AnalyticAt.analyticOrderAt_comp
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {g : 𝕜 → 𝕜} {z₀ : 𝕜},
AnalyticAt 𝕜 f (g z₀) →
AnalyticAt 𝕜 g z₀ → analyticOrderAt (f ∘ g) z₀ = analyticOrderAt f (g z₀) * analyticOrderAt (fun x => g x - g z₀) z₀Analytic order of a composition of analytic functions.
- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsproof · cited by 5,554
- ENatstatement and proof · cited by 4,985
- Filter.Eventuallyproof · cited by 3,134
- mul_commproof · cited by 2,262
- Filter.univ_mem'proof · cited by 1,672
- MulZeroClass.zero_mulproof · cited by 1,625
- Filter.mp_memproof · cited by 1,537
- sub_zeroproof · cited by 938
Cited by1
Results whose statement or proof uses this declaration.
- analyticOrderAt_comp_of_deriv_ne_zeroproof · cited by 0