Theorems · Theorem · several complex variables
hasFPowerSeriesOnBall_const
∀ {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] {c : F} {e : E},
HasFPowerSeriesOnBall (fun x => c) (constFormalMultilinearSeries 𝕜 E c) e ⊤- Defined in
- Mathlib.Analysis.Analytic.Constructions
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- SummationFilter.unconditionalproof · cited by 2,068
- Metric.eballproof · cited by 294
- zero_applyproof · cited by 251
- HasFPowerSeriesOnBallstatement · cited by 131
- constFormalMultilinearSeriesstatement · cited by 17
- hasSum_singleproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zeroproof · cited by 1
- hasFiniteFPowerSeriesOnBall_constproof · cited by 1
- hasFPowerSeriesAt_constproof · cited by 1
- analyticWithinAt_of_singleton_memproof · cited by 0