Theorems · Theorem · complex analysis
binomialSeries_eq_ordinaryHypergeometricSeries
∀ {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 b : 𝕂},
(∀ (k : ℕ), ↑k ≠ -b) →
binomialSeries 𝔸 a = (ordinaryHypergeometricSeries 𝔸 (-a) b b).compContinuousLinearMap (-ContinuousLinearMap.id 𝕂 𝔸)- Defined in
- Mathlib.Analysis.Analytic.Binomial
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- ContinuousLinearMapstatement · cited by 5,352
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- CharZerostatement and proof · cited by 932
- pow_oneproof · cited by 894
- Polynomial.evalproof · cited by 796
Cited by2
Results whose statement or proof uses this declaration.
- binomialSeries_radius_eq_oneproof · cited by 1
- binomialSeries_radius_eq_top_of_natproof · cited by 1