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Theorems · Theorem · complex analysis

MeromorphicAt.iterated_deriv

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

Iterated derivatives of meromorphic functions are meromorphic.

Defined in
Mathlib.Analysis.Meromorphic.Basic
Cited by
2 results in Mathlib
Foundations
Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeromorphicOn.iterated_deriv · cited by 0MeromorphicOn.iterated_de…Meromorphic.iterated_deriv · cited by 0Meromorphic.iterated_derivNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldCompleteSpace · cited by 2532CompleteSpaceNat.iterate · cited by 740Nat.iteratederiv · cited by 676derivMeromorphicAt · cited by 160MeromorphicAtFunction.iterate_succ' · cited by 56Function.iterate_succ'MeromorphicAt.deriv · cited by 6MeromorphicAt.derivMeromorphicAt.iterated_derivCITED BYCITES

Cites9

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Cited by2

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