Theorems · Theorem · complex analysis

MeromorphicAt.meromorphicTrailingCoeffAt_of_order_eq_top

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜}, meromorphicOrderAt f x = ⊤ → meromorphicTrailingCoeffAt f x = 0

If f is meromorphic of infinite order at x, the trailing coefficient is zero by definition.

Defined in

Mathlib.Analysis.Meromorphic.TrailingCoefficient

Cited by

11 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace