Theorems · Theorem · global analysis
taylor_tendsto
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℝ → E} {x₀ : ℝ} {n : ℕ} {s : Set ℝ},
Convex ℝ s →
x₀ ∈ s →
ContDiffOn ℝ (↑n) f s →
Filter.Tendsto (fun x => ((x - x₀) ^ n)⁻¹ • (f x - taylorWithinEval f n s x₀ x)) (nhdsWithin x₀ s) (nhds 0)Taylor's theorem as a limit.
- Defined in
- Mathlib.Analysis.Calculus.Taylor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- nhdsstatement and proof · cited by 5,554
- Norm.normproof · cited by 5,413
- ENatstatement · cited by 4,985
- Filter.Tendstostatement and proof · cited by 3,814
- WithTopstatement · cited by 3,754
- nhdsWithinstatement and proof · cited by 1,912
- absproof · cited by 1,814
- sub_selfproof · cited by 996
Cited by1
Results whose statement or proof uses this declaration.
- Real.taylor_tendstoproof · cited by 0