Theorems · Theorem · complex analysis

AnalyticAt.meromorphicTrailingCoeffAt_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},
  AnalyticAt 𝕜 g x →
    (f =ᶠ[nhdsWithin x {x}ᶜ] fun z => (z - x) ^ (meromorphicOrderAt f x).untop₀ • g z) →
      meromorphicTrailingCoeffAt f x = g x

Definition of the trailing coefficient in case where f is meromorphic and a presentation of the form f = (z - x) ^ order • g z is given, with g analytic at x.

Defined in

Mathlib.Analysis.Meromorphic.TrailingCoefficient

Cited by

4 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace