Theorems · Theorem · complex analysis

FormalMultilinearSeries.hasSum

∀ {𝕜 : Type u_1} {E : Type u_3} {F : Type u_4} [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 : E},
  x ∈ Metric.eball 0 p.radius → HasSum (fun n => (p n) fun x_1 => x) (p.sum x)

Defined in

Mathlib.Analysis.Analytic.ConvergenceRadius

Cited by

5 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace