Theorems · Theorem · several complex variables

AnalyticOnNhd.zpow

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {𝕝 : Type u_8} [inst_3 : NormedDivisionRing 𝕝] [inst_4 : NormedAlgebra 𝕜 𝕝] {f : E → 𝕝}
  {s : Set E} {n : ℤ}, AnalyticOnNhd 𝕜 f s → (∀ z ∈ s, f z ≠ 0) → AnalyticOnNhd 𝕜 (f ^ n) s

ZPowers of analytic functions (into a normed field over 𝕜) are analytic away from the zeros.

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

1 results in Mathlib

Foundations

Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedDivisionRingNormedAlgebra