Theorems · Theorem · complex analysis

fun_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 (fun i => f i / g i) x = meromorphicOrderAt f x - meromorphicOrderAt g x

Eta-expanded form of meromorphicOrderAt_div The order of a quotient is the difference of the orders.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra