Theorems · Theorem · complex analysis

tendsto_cobounded_iff_meromorphicOrderAt_neg

∀ {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 → (Filter.Tendsto f (nhdsWithin x {x}ᶜ) (Bornology.cobounded E) ↔ meromorphicOrderAt f x < 0)

A meromorphic function converges to infinity iff its order is negative.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

0 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace