Theorems · Theorem · complex analysis

AnalyticAt.meromorphicTrailingCoeffAt_of_ne_zero_of_eq_nhdsNE

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f g : 𝕜 → E} {x : 𝕜} {n : ℤ},
  AnalyticAt 𝕜 g x →
    g x ≠ 0 → (f =ᶠ[nhdsWithin x {x}ᶜ] fun z => (z - x) ^ n • g z) → meromorphicTrailingCoeffAt f x = g x

Variant of meromorphicTrailingCoeffAt_of_order_eq_finite: Definition of the trailing coefficient in case where f is meromorphic of finite order and a presentation is given.

Defined in

Mathlib.Analysis.Meromorphic.TrailingCoefficient

Cited by

11 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace