Theorems · Theorem · several complex variables

AnalyticWithinAt.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}
  {z : E} {s : Set E} {n : ℤ}, AnalyticWithinAt 𝕜 f s z → f z ≠ 0 → AnalyticWithinAt 𝕜 (f ^ n) s z

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

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

2 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedDivisionRingNormedAlgebra