Theorems · Theorem · several complex variables

FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] [CompleteSpace F]
  (p : FormalMultilinearSeries 𝕜 E F) (k : ℕ),
  0 < p.radius → HasFPowerSeriesOnBall (fun x => p.changeOrigin x k) (p.changeOriginSeries k) 0 p.radius

Defined in

Mathlib.Analysis.Analytic.ChangeOrigin

Cited by

4 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace