Theorems · Theorem · complex analysis

MeromorphicOn.logDeriv_zpow_eventuallyEq

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {𝕜' : Type u_2} [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {f : 𝕜 → 𝕜'} {U : Set 𝕜},
  MeromorphicOn f U → ∀ (n : ℤ), logDeriv (f ^ n) =ᶠ[Filter.codiscreteWithin U] n • logDeriv f

Away from a codiscrete subset of U, the logarithmic derivative of the n-th power of a meromorphic function is n times the logarithmic derivative.

Defined in

Mathlib.Analysis.Meromorphic.LogDeriv

Cited by

2 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra