Theorems · Theorem · complex analysis

meromorphicNFAt_smul_iff_right_of_analyticAt

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {g : 𝕜 → 𝕜} {x : 𝕜},
  AnalyticAt 𝕜 g x → g x ≠ 0 → (MeromorphicNFAt (g • f) x ↔ MeromorphicNFAt f x)

If f is any function and g is analytic without zero at z₀, then f is meromorphic in normal form at z₀ iff g • f is meromorphic in normal form at z₀.

Defined in

Mathlib.Analysis.Meromorphic.NormalForm

Cited by

3 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace