Theorems · Theorem · complex analysis
meromorphicOrderAt_logDeriv_eq_neg_one
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} [CompleteSpace 𝕜] {f : 𝕜 → 𝕜} [CharZero 𝕜],
MeromorphicAt f x → meromorphicOrderAt f x ≠ 0 → meromorphicOrderAt f x ≠ ⊤ → meromorphicOrderAt (logDeriv f) x = -1At zeros and poles of a meromorphic function f, the logarithmic derivative has a simple pole: its
meromorphic order equals -1.
- Defined in
- Mathlib.Analysis.Meromorphic.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- WithTopstatement and proof · cited by 3,754
- CompleteSpacestatement and proof · cited by 2,532
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- WithTop.someproof · cited by 1,128
- CharZerostatement and proof · cited by 932
- meromorphicOrderAtstatement and proof · cited by 180
- MeromorphicAtstatement and proof · cited by 160
- logDerivstatement · cited by 71
- sub_sub_cancel_leftproof · cited by 28
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.