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Theorems · Theorem · complex analysis

MeromorphicAt.meromorphicTrailingCoeffAt_mul

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {f₁ f₂ : 𝕜 → 𝕜},
  MeromorphicAt f₁ x →
    MeromorphicAt f₂ x →
      meromorphicTrailingCoeffAt (f₁ * f₂) x = meromorphicTrailingCoeffAt f₁ x * meromorphicTrailingCoeffAt f₂ x

The trailing coefficient of a product is the product of the trailing coefficients.

Defined in
Mathlib.Analysis.Meromorphic.TrailingCoefficient
Cited by
3 results in Mathlib
Foundations
Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedField
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Around this declaration

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meromorphicTrailingCoeffAt_prod · cited by 3meromorphicTrailingCoeffA…Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAt · cited by 1ECanonicalDecomp.eq_smul_…meromorphicTrailingCoeffAt_inv · cited by 1meromorphicTrailingCoeffA…NontriviallyNormedField · cited by 8742NontriviallyNormedFieldMeromorphicAt · cited by 160MeromorphicAtmeromorphicTrailingCoeffAt · cited by 61meromorphicTrailingCoeffAtMeromorphicAt.meromorphicTrailingCoeffAt_smul · cited by 7MeromorphicAt.meromorphic…MeromorphicAt.meromorphicTrai…CITED BYCITES

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Cited by3

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