Theorems · Theorem · global analysis

HasFPowerSeriesWithinAt.fderivWithin_eq

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type v} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  {p : FormalMultilinearSeries 𝕜 E F} {f : E → F} {x : E} {s : Set E},
  HasFPowerSeriesWithinAt f p s x →
    UniqueDiffWithinAt 𝕜 (insert x s) x → fderivWithin 𝕜 f (insert x s) x = (continuousMultilinearCurryFin1 𝕜 E F) (p 1)

Defined in

Mathlib.Analysis.Calculus.FDeriv.Analytic

Cited by

0 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace