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Theorems · Theorem · global analysis

HasFPowerSeriesAt.hasStrictDerivAt

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {p : FormalMultilinearSeries 𝕜 𝕜 F} {f : 𝕜 → F} {x : 𝕜},
  HasFPowerSeriesAt f p x → HasStrictDerivAt f ((p 1) fun x => 1) x
Defined in
Mathlib.Analysis.Calculus.FDeriv.Analytic
Cited by
1 results in Mathlib
Foundations
Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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Around this declaration

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

HasFPowerSeriesAt.hasDerivAt · cited by 1HasFPowerSeriesAt.hasDeri…DFunLike.coe · cited by 62936DFunLike.coeNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousMultilinearMap · cited by 1016ContinuousMultilinearMapFormalMultilinearSeries · cited by 615FormalMultilinearSeriesHasStrictDerivAt · cited by 163HasStrictDerivAtHasFPowerSeriesAt · cited by 94HasFPowerSeriesAtHasStrictFDerivAt.hasStrictDerivAt · cited by 18HasStrictFDerivAt.hasStri…HasFPowerSeriesAt.hasStrictFDerivAt · cited by 7HasFPowerSeriesAt.hasStri…HasFPowerSeriesAt.hasStrictDe…CITED BYCITES

Cites10

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Cited by1

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