Theorems · Theorem · complex analysis
FormalMultilinearSeries.radius_inv_eq_limsup
- 1000+ list: Cauchy–Hadamard theorem
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
(p : FormalMultilinearSeries 𝕜 E F), p.radius⁻¹ = Filter.limsup (fun n => ↑(‖p n‖₊ ^ (1 / ↑n))) Filter.atTopThe Cauchy-Hadamard theorem for formal multilinear series: The inverse of the radius is equal to $\limsup_{n\to\infty} \sqrt[n]{‖p n‖}$.
- Defined in
- Mathlib.Analysis.Analytic.RadiusLiminf
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- NNRealstatement · cited by 4,310
- Filter.atTopstatement and proof · cited by 2,405
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- ContinuousMultilinearMapstatement · cited by 1,016
- NNNorm.nnnormstatement and proof · cited by 952
- one_divproof · cited by 624
- FormalMultilinearSeriesstatement and proof · cited by 615
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