Theorems · Theorem · complex analysis
MeromorphicAt.meromorphicTrailingCoeffAt_zpow
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {n : ℤ} {f : 𝕜 → 𝕜},
MeromorphicAt f x → meromorphicTrailingCoeffAt (f ^ n) x = meromorphicTrailingCoeffAt f x ^ nThe trailing coefficient of the power of a function is the power of the trailing coefficient.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontriviallyNormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Compl.complproof · cited by 2,925
- mul_commproof · cited by 2,262
- nhdsWithinproof · cited by 1,912
- Filter.EventuallyEqproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- WithTop.someproof · cited by 1,128
- GroupWithZeroproof · cited by 691
- AnalyticAtproof · cited by 321
- meromorphicOrderAtproof · cited by 180
Cited by5
Results whose statement or proof uses this declaration.
- MeromorphicAt.meromorphicTrailingCoeffAt_compproof · cited by 1
- Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAtproof · cited by 1
- MeromorphicAt.meromorphicTrailingCoeffAt_powproof · cited by 1
- MeromorphicAt.meromorphicTrailingCoeffAt_fun_zpowproof · cited by 0