Theorems · Theorem · several complex variables

HasFiniteFPowerSeriesOnBall.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] {f : E → F}
  {p : FormalMultilinearSeries 𝕜 E F} {r : ENNReal} {n : ℕ} {x y : E},
  HasFiniteFPowerSeriesOnBall f p x n r →
    ↑‖y‖₊ < r → HasFiniteFPowerSeriesOnBall f (p.changeOrigin y) (x + y) n (r - ↑‖y‖₊)

Defined in

Mathlib.Analysis.Analytic.CPolynomialDef

Cited by

2 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace