Theorems · Theorem · complex analysis
FormalMultilinearSeries.ofScalars_comp_neg_id
∀ {𝕜 : Type u_1} (E : Type u_2) [inst : Field 𝕜] [inst_1 : Ring E] [inst_2 : Algebra 𝕜 E] [inst_3 : TopologicalSpace E]
[inst_4 : IsTopologicalRing E] (c : ℕ → 𝕜),
(FormalMultilinearSeries.ofScalars E c).compContinuousLinearMap (-ContinuousLinearMap.id 𝕜 E) =
FormalMultilinearSeries.ofScalars E fun k => (-1) ^ k * c k- Defined in
- Mathlib.Analysis.Analytic.OfScalars
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Monoidproof · cited by 3,887
- one_mulproof · cited by 2,841
- neg_mulproof · cited by 654
- FormalMultilinearSeriesstatement · cited by 615
- Evenproof · cited by 444
Cited by3
Results whose statement or proof uses this declaration.
- binomialSeries_eq_ordinaryHypergeometricSeriesproof · cited by 2
- alternatingGeometricSeries_eq_formalMultilinearSeries_geometric_comp_negproof · cited by 2
- FormalMultilinearSeries.ofScalars_comp_negproof · cited by 0