Theorems · Theorem · complex analysis
analyticOrderAt_iterated_deriv
∀ {𝕜 : Type u_3} {E : Type u_4} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [CompleteSpace E] {f : 𝕜 → E} {z₀ : 𝕜},
AnalyticAt 𝕜 f z₀ →
∀ {k n : ℕ} [CharZero 𝕜], ↑n = analyticOrderAt f z₀ → n ≠ 0 → k ≤ n → analyticOrderAt (deriv^[k] f) z₀ = ↑(n - k)- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement · cited by 4,985
- CompleteSpacestatement and proof · cited by 2,532
- Nat.cast_oneproof · cited by 2,501
- CharZerostatement and proof · cited by 932
- Nat.iteratestatement and proof · cited by 740
- derivstatement and proof · cited by 676
- Nat.cast_addproof · cited by 586
- AnalyticAtstatement and proof · cited by 321
- analyticOrderAtstatement and proof · cited by 69
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