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Theorems · Theorem · complex analysis

MeromorphicOn.iterated_deriv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {U : Set 𝕜},
  MeromorphicOn f U → ∀ [CompleteSpace E] {n : ℕ}, MeromorphicOn (deriv^[n] f) U

Iterated derivatives of meromorphic functions are meromorphic.

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
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpace
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Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldCompleteSpace · cited by 2532CompleteSpaceNat.iterate · cited by 740Nat.iteratederiv · cited by 676derivMeromorphicOn · cited by 141MeromorphicOnMeromorphicAt.iterated_deriv · cited by 2MeromorphicAt.iterated_de…MeromorphicOn.iterated_derivCITED BYCITES

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