Theorems · Theorem · complex analysis

MeromorphicOn.divisor_apply

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {U : Set 𝕜} {z : 𝕜} {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E},
  MeromorphicOn f U → z ∈ U → (MeromorphicOn.divisor f U) z = (meromorphicOrderAt f z).untop₀

Simplifier lemma: on U, the divisor of a function f that is meromorphic on U evaluates to order.untop₀.

Defined in

Mathlib.Analysis.Meromorphic.Divisor

Cited by

28 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace