Theorems · Theorem · several complex variables

HasFPowerSeriesOnBall.unshift

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} {F : Type u_4} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → E →L[𝕜] F}
  {pf : FormalMultilinearSeries 𝕜 E (E →L[𝕜] F)} {x : E} {r : ENNReal} {z : F},
  HasFPowerSeriesOnBall f pf x r → HasFPowerSeriesOnBall (fun y => z + (f y) (y - x)) (pf.unshift z) x r

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

0 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace