Theorems · Theorem · complex analysis
analyticOrderAt_smul
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {g : 𝕜 → E} {z₀ : 𝕜} {f : 𝕜 → 𝕜},
AnalyticAt 𝕜 f z₀ → AnalyticAt 𝕜 g z₀ → analyticOrderAt (f • g) z₀ = analyticOrderAt f z₀ + analyticOrderAt g z₀The order is additive when scalar multiplying analytic functions.
- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- 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
- Algebra.algebraMapproof · cited by 4,706
- Nat.cast_oneproof · cited by 2,501
- IsOpenproof · cited by 2,400
- Filter.EventuallyEqproof · cited by 1,912
- AnalyticAtstatement and proof · cited by 321
Cited by1
Results whose statement or proof uses this declaration.
- analyticOrderAt_mulproof · cited by 1