Theorems · Theorem · real analysis

iteratedDeriv_comp_add_const

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] (n : ℕ) (f : 𝕜 → F) (s : 𝕜),
  (iteratedDeriv n fun z => f (z + s)) = fun t => iteratedDeriv n f (t + s)

The iterated derivative commutes with shifting the function by a constant on the right.

Defined in

Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace