Theorems · Theorem · complex analysis

MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt

∀ {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 → (0 ≤ meromorphicOrderAt f x ↔ AnalyticAt 𝕜 f x)

If a function is meromorphic in normal form at x, then it has non-negative order iff it is analytic.

Defined in

Mathlib.Analysis.Meromorphic.NormalForm

Cited by

5 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace