Theorems · Theorem · several complex variables

HasFPowerSeriesOnBall.add

∀ {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 g : E → F}
  {pf pg : FormalMultilinearSeries 𝕜 E F} {x : E} {r : ENNReal},
  HasFPowerSeriesOnBall f pf x r → HasFPowerSeriesOnBall g pg x r → HasFPowerSeriesOnBall (f + g) (pf + pg) x r

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

5 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace