Theorems · Theorem · complex analysis
meromorphicAt_of_meromorphicOrderAt_ne_zero
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜}, meromorphicOrderAt f x ≠ 0 → MeromorphicAt f x- Defined in
- Mathlib.Analysis.Meromorphic.Order
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- WithTopstatement · cited by 3,754
- meromorphicOrderAtstatement and proof · cited by 180
- MeromorphicAtstatement and proof · cited by 160
- meromorphicOrderAt_of_not_meromorphicAtproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- tendsto_zero_of_meromorphicOrderAt_posproof · cited by 4
- tendsto_cobounded_of_meromorphicOrderAt_negproof · cited by 3
- meromorphicOrderAt_deriv_eq_sub_oneproof · cited by 2
- AnalyticAt.of_meromorphicOrderAt_posproof · cited by 0