Theorems · Theorem · complex analysis

meromorphicOrderAt_const

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] (z₀ : 𝕜) (e : E) [inst_3 : Decidable (e = 0)],
  meromorphicOrderAt (fun x => e) z₀ = if e = 0 then ⊤ else 0

The order of a constant function is ⊤ if the constant is zero and 0 otherwise.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

7 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceDecidable