Theorems · Theorem · complex analysis
FormalMultilinearSeries.ofScalars_apply_eq
∀ {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) (x : E) (n : ℕ),
((FormalMultilinearSeries.ofScalars E c n) fun x_1 => x) = c n • x ^ n- Defined in
- Mathlib.Analysis.Analytic.OfScalars
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- ContinuousMultilinearMapstatement · cited by 1,016
- IsTopologicalRingstatement and proof · cited by 402
- smul_applyproof · cited by 229
- FormalMultilinearSeries.ofScalarsstatement · cited by 68
- ContinuousMultilinearMap.mkPiAlgebraFinproof · cited by 29
- List.prod_replicateproof · cited by 29
- List.ofFn_constproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- PeriodPair.hasFPowerSeriesOnBall_weierstrassPExceptproof · cited by 3
- FormalMultilinearSeries.ofScalars_sum_eqproof · cited by 3
- ordinaryHypergeometricSeries_apply_eqproof · cited by 1
- ordinaryHypergeometricSeries_apply_zeroproof · cited by 1