Theorems · Theorem · complex analysis

meromorphicNFAt_mul_iff_left

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {g : 𝕜 → 𝕜} {x : 𝕜} {f : 𝕜 → 𝕜},
  AnalyticAt 𝕜 g x → g x ≠ 0 → (MeromorphicNFAt (f * g) 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 f * g is meromorphic in normal form at z₀.

Defined in

Mathlib.Analysis.Meromorphic.NormalForm

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedField