Theorems · Theorem · complex analysis
HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {p : FormalMultilinearSeries 𝕜 𝕜 E} {f : 𝕜 → E} {z₀ : 𝕜},
HasFPowerSeriesAt f p z₀ → ∀ (z : 𝕜), f z = (z - z₀) ^ p.order • (Function.swap dslope z₀)^[p.order] f z- Defined in
- Mathlib.Analysis.Analytic.IsolatedZeros
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- zero_addproof · cited by 2,366
- ContinuousMultilinearMapproof · cited by 1,016
- Nat.iteratestatement and proof · cited by 740
- FormalMultilinearSeriesstatement and proof · cited by 615
- zero_applyproof · cited by 251
- Function.swapstatement · cited by 216
- HasFPowerSeriesAtstatement and proof · cited by 94
- dslopestatement · cited by 40
Cited by2
Results whose statement or proof uses this declaration.
- AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iffproof · cited by 3
- HasFPowerSeriesAt.locally_ne_zeroproof · cited by 1