Theorems · Theorem · complex analysis
MeromorphicAt.meromorphicTrailingCoeffAt_smul
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {x : 𝕜} {f₁ : 𝕜 → 𝕜} {f₂ : 𝕜 → E},
MeromorphicAt f₁ x →
MeromorphicAt f₂ x →
meromorphicTrailingCoeffAt (f₁ • f₂) x = meromorphicTrailingCoeffAt f₁ x • meromorphicTrailingCoeffAt f₂ xThe trailing coefficient of a scalar product is the scalar product of the trailing coefficients.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Algebra.algebraMapproof · cited by 4,706
- Compl.complproof · cited by 2,925
- Nat.cast_oneproof · cited by 2,501
- 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
- zero_smulproof · cited by 716
Cited by7
Results whose statement or proof uses this declaration.
- MeromorphicAt.meromorphicTrailingCoeffAt_mulproof · cited by 3
- MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_polesproof · cited by 1
- Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAtproof · cited by 1
- MeromorphicAt.meromorphicTrailingCoeffAt_compproof · cited by 1
- MeromorphicAt.meromorphicTrailingCoeffAt_fun_mulproof · cited by 0
- MeromorphicAt.meromorphicTrailingCoeffAt_fun_smulproof · cited by 0
- MeromorphicOn.meromorphicTrailingCoeffAt_extract_zeros_polesproof · cited by 0