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Theorems · Theorem · complex analysis

MeromorphicOn.logDeriv

∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {U : Set 𝕜} [CompleteSpace 𝕜'] {f : 𝕜 → 𝕜'} {hf : MeromorphicOn f U},
  MeromorphicOn (logDeriv f) U

If f is meromorphic on a set, then so is its logarithmic derivative.

Defined in
Mathlib.Analysis.Meromorphic.Basic
Cited by
0 results in Mathlib
Foundations
Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebraCompleteSpace
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Set · cited by 53352SetNontriviallyNormedField · cited by 8742NontriviallyNormedFieldCompleteSpace · cited by 2532CompleteSpaceNormedAlgebra · cited by 1165NormedAlgebraMeromorphicOn · cited by 141MeromorphicOnlogDeriv · cited by 71logDerivMeromorphicOn.div · cited by 2MeromorphicOn.divMeromorphicOn.deriv · cited by 1MeromorphicOn.derivMeromorphicOn.logDerivCITED BYCITES

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