Theorems · Theorem · global analysis

HasFPowerSeriesOnBall.fderiv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type v} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  {p : FormalMultilinearSeries 𝕜 E F} {r : ENNReal} {f : E → F} {x : E} [CompleteSpace F],
  HasFPowerSeriesOnBall f p x r → HasFPowerSeriesOnBall (fderiv 𝕜 f) p.derivSeries x r

If a function has a power series on a ball, then so does its derivative.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Analytic

Cited by

4 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace