Theorems · Theorem · complex analysis
FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto
∀ {𝕜 : Type u_1} (E : Type u_2) [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedRing E] [inst_2 : NormedAlgebra 𝕜 E]
(c : ℕ → 𝕜) [NormOneClass E],
Filter.Tendsto (fun n => ‖c n.succ‖ / ‖c n‖) Filter.atTop Filter.atTop →
(FormalMultilinearSeries.ofScalars E c).radius = 0If ‖c n.succ‖ / ‖c n‖ is unbounded, then the radius of convergence is zero.
- Defined in
- Mathlib.Analysis.Analytic.OfScalars
- Cited by
- 1 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.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- NNRealproof · cited by 4,310
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- Filter.atTopstatement and proof · cited by 2,405
- mul_commproof · cited by 2,262
- SummationFilter.unconditionalproof · cited by 2,068
- Filter.univ_mem'proof · cited by 1,672
- mul_assocproof · cited by 1,667
Cited by1
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNRealproof · cited by 0