Theorems · Theorem · complex analysis

AnalyticAt.aeval_mvPolynomial

∀ {𝕜 : Type u_1} {E : Type u_2} {A : Type u_3} {B : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : CommSemiring A] {z : E}
  [inst_4 : NormedCommRing B] [inst_5 : NormedAlgebra 𝕜 B] [inst_6 : Algebra A B] {σ : Type u_5} {f : E → σ → B},
  (∀ (i : σ), AnalyticAt 𝕜 (fun x => f x i) z) →
    ∀ (p : MvPolynomial σ A), AnalyticAt 𝕜 (fun x => (MvPolynomial.aeval (f x)) p) z

Defined in

Mathlib.Analysis.Analytic.Polynomial

Cited by

3 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCommSemiringNormedCommRingNormedAlgebraAlgebra