Theorems · Theorem · commutative algebra
PowerSeries.coeff_prod
∀ {R : Type u_2} [inst : CommSemiring R] {ι : Type u_3} [inst_1 : DecidableEq ι] (f : ι → PowerSeries R) (d : ℕ)
(s : Finset ι),
(PowerSeries.coeff d) (∏ j ∈ s, f j) = ∑ l ∈ s.finsuppAntidiag d, ∏ i ∈ s, (PowerSeries.coeff (l i)) (f i)Coefficients of a product of power series
- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
- Finset.prodstatement and proof · cited by 2,356
- Finsupp.singleproof · cited by 943
- PowerSeriesstatement and proof · cited by 797
- AddEquiv.symmproof · cited by 530
- PowerSeries.coeffstatement · cited by 324
Cited by2
Results whose statement or proof uses this declaration.
- Nat.Partition.hasProd_genFunproof · cited by 4
- PowerSeries.coeff_powproof · cited by 0