Theorems · Theorem · complex analysis

meromorphicOrderAt_zpow

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {𝕜' : Type u_4} [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {f : 𝕜 → 𝕜'} {x : 𝕜},
  MeromorphicAt f x → ∀ {n : ℤ}, meromorphicOrderAt (f ^ n) x = ↑n * meromorphicOrderAt f x

The order multiplies by n when taking a meromorphic function to its nth power.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

4 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra