Theorems · Definition · commutative algebra
PowerSeries.binomialSeries
{R : Type u_1} → [inst : CommRing R] → [BinomialRing R] → (A : Type u_3) → [One A] → [SMul R A] → R → PowerSeries AThe power series for (1 + X) ^ r.
- Defined in
- Mathlib.RingTheory.PowerSeries.Binomial
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingBinomialRingOneSMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- PowerSeriesstatement · cited by 797
- PowerSeries.mkproof · cited by 52
- BinomialRingstatement and proof · cited by 46
- Ring.chooseproof · cited by 43
Cited by11
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.binomialFamilyproof · cited by 8
- PowerSeries.binomialSeries_coeffstatement · cited by 7
- HahnSeries.SummableFamily.binomialFamily_applyproof · cited by 3
- HahnSeries.SummableFamily.binomialFamily_orderTop_posproof · cited by 2
- PowerSeries.binomialSeries_addstatement and proof · cited by 1
- PowerSeries.binomialSeries_natstatement and proof · cited by 1
- HahnSeries.pow_addproof · cited by 0
- PowerSeries.binomialSeries_constantCoeffstatement and proof · cited by 0
- PowerSeries.binomialSeries_zerostatement and proof · cited by 0
- HahnSeries.SummableFamily.binomialFamily_apply_of_orderTop_nonposproof · cited by 0
- PowerSeries.rescale_neg_one_invOneSubPowstatement and proof · cited by 0