Theorems · Theorem · complex analysis

HasFPowerSeriesAt.apply_eq_zero

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  {p : FormalMultilinearSeries 𝕜 E F} {x : E}, HasFPowerSeriesAt 0 p x → ∀ (n : ℕ) (y : E), ((p n) fun x => y) = 0

If a formal multilinear series p represents the zero function at x : E, then the terms p n (fun i ↦ y) appearing in the sum are zero for any n : ℕ, y : E.

Defined in

Mathlib.Analysis.Analytic.Uniqueness

Cited by

2 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace