Theorems · Theorem · functional analysis
FormalMultilinearSeries.apply_eq_prod_smul_coeff
∀ {𝕜 : Type u} {E : Type v} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {p : FormalMultilinearSeries 𝕜 𝕜 E} {n : ℕ} {y : Fin n → 𝕜},
(p n) y = (∏ i, y i) • p.coeff n- Cited by
- 19 results in Mathlib
- Foundations
- Depth 168 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 and proof · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- mul_oneproof · cited by 3,885
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- ContinuousMultilinearMapstatement · cited by 1,016
- FormalMultilinearSeriesstatement and proof · cited by 615
- ContinuousMultilinearMap.toMultilinearMapproof · cited by 70
- FormalMultilinearSeries.coeffstatement and proof · cited by 30
- MultilinearMap.map_smul_univproof · cited by 8
Cited by19
Results whose statement or proof uses this declaration.
- AnalyticAt.hasFPowerSeriesAtproof · cited by 7
- Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- AnalyticAt.analyticAt_localInverseproof · cited by 2
- Real.one_div_sub_pow_hasFPowerSeriesOnBall_zeroproof · cited by 2
- hasFPowerSeriesAt_clog_oneproof · cited by 2
- HasFPowerSeriesAt.iterate_dslope_fslope_ne_zeroproof · cited by 2
- Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 2
- Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zeroproof · cited by 1
- PeriodPair.weierstrassPExcept_eq_tsumproof · cited by 1
- PeriodPair.hasFPowerSeriesOnBall_derivWeierstrassPExceptproof · cited by 1
- hasFPowerSeriesAt_iffproof · cited by 1