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Theorems · Theorem · global analysis

AnalyticAt.iterated_deriv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} [CompleteSpace F],
  AnalyticAt 𝕜 f x → ∀ (n : ℕ), AnalyticAt 𝕜 (deriv^[n] f) x
Defined in
Mathlib.Analysis.Calculus.FDeriv.Analytic
Cited by
1 results in Mathlib
Foundations
Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

analyticOrderAt_iterated_deriv · cited by 0analyticOrderAt_iterated_…NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldCompleteSpace · cited by 2532CompleteSpaceNat.iterate · cited by 740Nat.iteratederiv · cited by 676derivAnalyticAt · cited by 321AnalyticAtFunction.iterate_succ' · cited by 56Function.iterate_succ'AnalyticAt.deriv · cited by 10AnalyticAt.derivAnalyticAt.iterated_derivCITED BYCITES

Cites9

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Cited by1

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