Theorems · Theorem · complex analysis

meromorphicOrderAt_div

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {𝕜' : Type u_4} [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {x : 𝕜} {f g : 𝕜 → 𝕜'},
  MeromorphicAt f x → MeromorphicAt g x → meromorphicOrderAt (f / g) x = meromorphicOrderAt f x - meromorphicOrderAt g x

The order of a quotient is the difference of the orders.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra