Theorems · Definition · several complex variables

AnalyticAt

(𝕜 : Type u_1) →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : NontriviallyNormedField 𝕜] →
        [inst_1 : NormedAddCommGroup E] →
          [NormedSpace 𝕜 E] → [inst_3 : NormedAddCommGroup F] → [NormedSpace 𝕜 F] → (E → F) → E → Prop

Given a function f : E → F, we say that f is analytic at x if it admits a convergent power series expansion around x.

Defined in

Mathlib.Analysis.Analytic.Basic

Cited by

321 results in Mathlib

Foundations

Depth 165 from the axioms, rests on 3,365 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace