Theorems · Theorem · complex analysis

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

If the order of a meromorphic function is negative, then this function converges to infinity at this point. See also the iff version tendsto_cobounded_iff_meromorphicOrderAt_neg.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

3 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace