Theorems · Theorem · complex analysis
MeromorphicNFAt.meromorphicAt
∀ {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}, MeromorphicNFAt f x → MeromorphicAt f xIf a function is meromorphic in normal form at x, then it is meromorphic at x.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 198 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
- AnalyticAtproof · cited by 321
- meromorphicOrderAtproof · cited by 180
- MeromorphicAtstatement and proof · cited by 160
- MeromorphicNFAtstatement and proof · cited by 34
- AnalyticAt.meromorphicAtproof · cited by 22
- meromorphicNFAt_iff_analyticAt_orproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- MeromorphicNFAt.meromorphicOrderAt_eq_zero_iffproof · cited by 14
- MeromorphicNFOn.meromorphicOnproof · cited by 13
- toMeromorphicNFAt_eq_selfproof · cited by 4
- Complex.meromorphicAt_tanproof · cited by 1
- Complex.meromorphicAt_tanhproof · cited by 1
- MeromorphicOn.exists_canonicalDecompproof · cited by 1
- Complex.CanonicalDecomp.divisor_eq_divisorproof · cited by 1