Theorems · Theorem · real analysis
isSymmSndFDerivAt_iff_iteratedFDeriv
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} {F : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x : E},
IsSymmSndFDerivAt 𝕜 f x ↔
ContinuousMultilinearMap.domDomCongr Fin.revPerm (iteratedFDeriv 𝕜 2 f x) = iteratedFDeriv 𝕜 2 f x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousMultilinearMapstatement · cited by 1,016
- Set.mem_univproof · cited by 416
- iteratedFDerivstatement · cited by 211
- uniqueDiffOn_univproof · cited by 66
- Fin.revPermstatement and proof · cited by 25
- ContinuousMultilinearMap.domDomCongrstatement and proof · cited by 16
- IsSymmSndFDerivAtstatement · cited by 10
- isSymmSndFDerivWithinAt_iff_iteratedFDerivWithinproof · cited by 3
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