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Theorems · Theorem · complex analysis

MeromorphicAt.fun_mul

∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {x : 𝕜} {f g : 𝕜 → 𝕜'},
  MeromorphicAt f x → MeromorphicAt g x → MeromorphicAt (fun i => f i * g i) x

Eta-expanded form of MeromorphicAt.mul

Defined in
Mathlib.Analysis.Meromorphic.Basic
Cited by
3 results in Mathlib
Foundations
Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeromorphicAt.deriv · cited by 6MeromorphicAt.derivComplex.meromorphic_canonicalFactor · cited by 5Complex.meromorphic_canon…Complex.meromorphicOrderAt_canonicalFactor · cited by 3Complex.meromorphicOrderA…NontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraMeromorphicAt · cited by 160MeromorphicAtMeromorphicAt.mul · cited by 7MeromorphicAt.mulMeromorphicAt.fun_mulCITED BYCITES

Cites4

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Cited by3

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