Theorems · Theorem · complex analysis
analyticOrderNatAt_pow
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {f : 𝕜 → 𝕜} {z₀ : 𝕜},
AnalyticAt 𝕜 f z₀ → ∀ (n : ℕ), analyticOrderNatAt (f ^ n) z₀ = n • analyticOrderNatAt f z₀The order multiplies by n when taking an analytic function to its nth power.
- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontriviallyNormedField
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- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nsmul_eq_mulproof · cited by 369
- AnalyticAtstatement and proof · cited by 321
- ENat.toNatproof · cited by 143
- analyticOrderAtproof · cited by 69
- analyticOrderNatAtstatement · cited by 9
- ENat.toNat_mulproof · cited by 4
- analyticOrderAt_powproof · cited by 1
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