Theorems · Theorem · several complex variables

AnalyticWithinAt.fun_pow

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {A : Type u_7} [inst_3 : NormedRing A] [inst_4 : NormedAlgebra 𝕜 A] {f : E → A} {z : E}
  {s : Set E}, AnalyticWithinAt 𝕜 f s z → ∀ (n : ℕ), AnalyticWithinAt 𝕜 (fun i => f i ^ n) s z

Eta-expanded form of AnalyticWithinAt.pow Powers of analytic functions (into a normed 𝕜-algebra) are analytic.

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

0 results in Mathlib

Foundations

Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedRingNormedAlgebra