Theorems · Theorem · complex analysis
binomialSeries_apply
∀ {𝕂 : Type u} [inst : Field 𝕂] [inst_1 : CharZero 𝕂] (𝔸 : Type v) [inst_2 : Ring 𝔸] [inst_3 : Algebra 𝕂 𝔸]
[inst_4 : TopologicalSpace 𝔸] [inst_5 : IsTopologicalRing 𝔸] (a : 𝕂) {n : ℕ} (v : Fin n → 𝔸),
(binomialSeries 𝔸 a n) v = Ring.choose a n • (List.ofFn v).prod- Defined in
- Mathlib.Analysis.Analytic.Binomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 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.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- ContinuousMultilinearMapstatement · cited by 1,016
- CharZerostatement and proof · cited by 932
- NNRatstatement · cited by 523
- IsTopologicalRingstatement and proof · cited by 402
- smul_applyproof · cited by 229
- Ring.choosestatement and proof · cited by 43
- ContinuousMultilinearMap.mkPiAlgebraFinproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- Real.one_add_rpow_hasFPowerSeriesOnBall_zeroproof · cited by 1