Theorems · Theorem · complex analysis
MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {x : 𝕜} {f : 𝕜 → E},
MeromorphicAt f x ↔ ∃ n g, AnalyticAt 𝕜 g x ∧ ∀ᶠ (z : 𝕜) in nhdsWithin x {x}ᶜ, f z = (z - x) ^ n • g z- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 1 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.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Filter.Eventuallystatement and proof · cited by 3,134
- Compl.complstatement and proof · cited by 2,925
- Nat.cast_oneproof · cited by 2,501
- nhdsWithinstatement and proof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.EventuallyEq.symmproof · cited by 408
Cited by1
Results whose statement or proof uses this declaration.
- MeromorphicAt.derivproof · cited by 6