Theorems · Theorem · functional analysis
FormalMultilinearSeries.coeff_iterate_fslope
∀ {𝕜 : Type u} {E : Type v} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {p : FormalMultilinearSeries 𝕜 𝕜 E} (k n : ℕ),
(FormalMultilinearSeries.fslope^[k] p).coeff n = p.coeff (n + k)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- add_assocproof · cited by 746
- Nat.iteratestatement and proof · cited by 740
- FormalMultilinearSeriesstatement and proof · cited by 615
- FormalMultilinearSeries.coeffstatement and proof · cited by 30
- FormalMultilinearSeries.fslopestatement and proof · cited by 6
- FormalMultilinearSeries.coeff_fslopeproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- HasFPowerSeriesAt.iterate_dslope_fslope_ne_zeroproof · cited by 2
- HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslopeproof · cited by 2