Theorems · Definition · several complex variables

HasFPowerSeriesAt

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : NontriviallyNormedField 𝕜] →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : NormedSpace 𝕜 E] →
            [inst_3 : NormedAddCommGroup F] →
              [inst_4 : NormedSpace 𝕜 F] → (E → F) → FormalMultilinearSeries 𝕜 E F → E → Prop

Given a function f : E → F and a formal multilinear series p, we say that f has p as a power series around x if f (x + y) = ∑' pₙ yⁿ for all y in a neighborhood of 0.

Defined in

Mathlib.Analysis.Analytic.Basic

Cited by

94 results in Mathlib

Foundations

Depth 164 from the axioms, rests on 3,364 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace