Theorems · Theorem · complex analysis
AnalyticAt.meromorphicNFAt
∀ {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}, AnalyticAt 𝕜 f x → MeromorphicNFAt f xAnalytic functions are meromorphic in normal form.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 199 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
- AnalyticAtstatement and proof · cited by 321
- meromorphicOrderAtproof · cited by 180
- MeromorphicAtproof · cited by 160
- MeromorphicNFAtstatement · cited by 34
Cited by16
Results whose statement or proof uses this declaration.
- meromorphicNFAt_toMeromorphicNFAtproof · cited by 5
- MeromorphicOn.meromorphicNFAt_mem_codiscreteWithinproof · cited by 4
- AnalyticOnNhd.meromorphicNFOnproof · cited by 3
- Complex.meromorphicOrderAt_canonicalFactorproof · cited by 3
- MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNEproof · cited by 3
- meromorphicNFAt_prodproof · cited by 3
- MeromorphicNFAt.zpowproof · cited by 2
- MeromorphicNFOn.divproof · cited by 2
- Complex.meromorphicNFOn_canonicalFactorproof · cited by 1
- Complex.meromorphicNFOn_tanproof · cited by 1
- Complex.meromorphicNFOn_tanhproof · cited by 1
- Complex.meromorphicOrderAt_canonicalFactor_ne_topproof · cited by 1