Theorems · Theorem · complex analysis
MeromorphicAt.zpow
∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜']
[inst_2 : NormedAlgebra 𝕜 𝕜'] {x : 𝕜} {f : 𝕜 → 𝕜'}, MeromorphicAt f x → ∀ (n : ℤ), MeromorphicAt (f ^ n) x- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- NormedAlgebrastatement and proof · cited by 1,165
- zpow_natCastproof · cited by 271
- MeromorphicAtstatement and proof · cited by 160
- zpow_negSuccproof · cited by 92
- MeromorphicAt.powproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_zpowproof · cited by 4
- meromorphicNFAt_iff_analyticAt_orproof · cited by 3
- meromorphicOrderAt_zpow_id_sub_constproof · cited by 3
- MeromorphicAt.fun_zpowproof · cited by 3
- MeromorphicOn.zpowproof · cited by 3
- meromorphicOrderAt_addproof · cited by 2
- MeromorphicAt.meromorphicOrderAt_compproof · cited by 2
- Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAtproof · cited by 1
- MeromorphicAt.meromorphicTrailingCoeffAt_compproof · cited by 1
- Meromorphic.zpowproof · cited by 1
- MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAtproof · cited by 1