Theorems · Theorem · several complex variables

FormalMultilinearSeries.changeOrigin_eval

∀ {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) {x y : E}, ↑‖x‖₊ + ↑‖y‖₊ < p.radius → (p.changeOrigin x).sum y = p.sum (x + y)

Summing the series p.changeOrigin x at a point y gives back p (x + y).

Defined in

Mathlib.Analysis.Analytic.ChangeOrigin

Cited by

1 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace