Theorems · Definition · complex analysis
binomialSeries
{𝕂 : Type u} →
[inst : Field 𝕂] →
[CharZero 𝕂] →
(𝔸 : Type v) →
[inst_2 : Ring 𝔸] →
[inst_3 : Algebra 𝕂 𝔸] →
[inst_4 : TopologicalSpace 𝔸] → [inst_5 : IsTopologicalRing 𝔸] → 𝕂 → FormalMultilinearSeries 𝕂 𝔸 𝔸Binomial series: the (scalar) formal multilinear series with coefficients given
by Ring.choose a. The sum of this series is fun x ↦ (1 + x) ^ a within the radius
of convergence.
- Defined in
- Mathlib.Analysis.Analytic.Binomial
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- CharZerostatement and proof · cited by 932
- FormalMultilinearSeriesstatement · cited by 615
- IsTopologicalRingstatement and proof · cited by 402
- FormalMultilinearSeries.ofScalarsproof · cited by 68
- Ring.chooseproof · cited by 43
Cited by11
Results whose statement or proof uses this declaration.
- Complex.one_add_cpow_hasFPowerSeriesOnBall_zerostatement and proof · cited by 3
- binomialSeries_eq_ordinaryHypergeometricSeriesstatement · cited by 2
- Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 2
- binomialSeries_applystatement · cited by 1
- binomialSeries_radius_eq_onestatement · cited by 1
- binomialSeries_radius_eq_top_of_natstatement · cited by 1
- binomialSeries_radius_ge_onestatement · cited by 1
- Real.one_add_rpow_hasFPowerSeriesOnBall_zerostatement and proof · cited by 1
- binomialSeries.congr_simpstatement and proof · cited by 0
- Real.one_add_rpow_hasFPowerSeriesAt_zerostatement · cited by 0
- Complex.one_add_cpow_hasFPowerSeriesAt_zerostatement · cited by 0