Theorems · Theorem · several complex variables
FormalMultilinearSeries.analyticOnNhd
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] [CompleteSpace F]
{p : FormalMultilinearSeries 𝕜 E F}, AnalyticOnNhd 𝕜 p.sum (Metric.eball 0 p.radius)Sum of series is analytic on its ball of convergence.
- Defined in
- Mathlib.Analysis.Analytic.ChangeOrigin
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- CompleteSpacestatement and proof · cited by 2,532
- FormalMultilinearSeriesstatement and proof · cited by 615
- Metric.eballstatement and proof · cited by 294
- AnalyticOnNhdstatement and proof · cited by 206
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
- FormalMultilinearSeries.sumstatement and proof · cited by 34
- pos_of_ne_zeroproof · cited by 21
- FormalMultilinearSeries.hasFPowerSeriesOnBallproof · cited by 7
- Metric.eball_zeroproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AnalyticOn.hasFPowerSeriesOnSubballproof · cited by 2