Theorems · Theorem · real analysis

iteratedFDerivWithin_comp_const_sub

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type uF} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {s : Set 𝕜} (n : ℕ) (c : 𝕜),
  iteratedFDerivWithin 𝕜 n (fun z => f (c - z)) s = fun x => (-1) ^ n • iteratedFDerivWithin 𝕜 n f (c +ᵥ -s) (c - x)

Defined in

Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries

Cited by

1 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace