Theorems · Theorem · complex analysis

meromorphicNFOn_smul_iff_right_of_analyticOnNhd

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {U : Set 𝕜} {g : 𝕜 → 𝕜},
  AnalyticOnNhd 𝕜 g U → (∀ u ∈ U, g u ≠ 0) → (MeromorphicNFOn (g • f) U ↔ MeromorphicNFOn f U)

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

Defined in

Mathlib.Analysis.Meromorphic.NormalForm

Cited by

1 results in Mathlib

Foundations

Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace