Theorems · Theorem · complex analysis
binomialSeries_radius_eq_one
∀ {𝕂 : Type v} [inst : RCLike 𝕂] {𝔸 : Type u} [inst_1 : NormedDivisionRing 𝔸] [inst_2 : NormedAlgebra 𝕂 𝔸] {a : 𝕂},
(∀ (k : ℕ), a ≠ ↑k) → (binomialSeries 𝔸 a).radius = 1The radius of convergence of binomialSeries 𝔸 a is 1, when a is not natural.
- Defined in
- Mathlib.Analysis.Analytic.Binomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpaceproof · cited by 24,529
- Algebraproof · cited by 11,388
- ENNRealstatement · cited by 9,879
- Ringproof · cited by 7,463
- RCLikestatement and proof · cited by 2,829
- Nat.cast_oneproof · cited by 2,501
- NormedAlgebrastatement and proof · cited by 1,165
- IsTopologicalRingproof · cited by 402
- Int.cast_natCastproof · cited by 393
- NormedDivisionRingstatement and proof · cited by 360
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
- ordinaryHypergeometricSeriesproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- binomialSeries_radius_ge_oneproof · cited by 1