Theorems · Theorem · several complex variables

AnalyticAt.fun_zpow_nonneg

∀ {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} {n : ℤ}, AnalyticAt 𝕜 f z → 0 ≤ n → AnalyticAt 𝕜 (fun i => f i ^ n) z

Eta-expanded form of AnalyticAt.zpow_nonneg ZPowers of analytic functions (into a normed division algebra over 𝕜) are analytic if the exponent is nonnegative.

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