Theorems · Theorem · real analysis

ContDiff.ftaylorSeries

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {n : WithTop ℕ∞}, ContDiff 𝕜 n f → HasFTaylorSeriesUpTo n f (ftaylorSeries 𝕜 f)

When a function is C^n, it admits ftaylorSeries 𝕜 f as a Taylor series up to order n in s.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Defs

Cited by

1 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace