Theorems · Theorem · complex analysis
tendsto_ne_zero_iff_meromorphicOrderAt_eq_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},
MeromorphicAt f x → ((∃ c, c ≠ 0 ∧ Filter.Tendsto f (nhdsWithin x {x}ᶜ) (nhds c)) ↔ meromorphicOrderAt f x = 0)A meromorphic function converges to a nonzero limit iff its order is zero.
- Defined in
- Mathlib.Analysis.Meromorphic.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
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
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- WithTopstatement · cited by 3,754
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- eq_or_neproof · cited by 1,117
- meromorphicOrderAtstatement and proof · cited by 180
- MeromorphicAtstatement and proof · cited by 160
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