Theorems · Inductive type · several complex variables

HasFiniteFPowerSeriesOnBall

{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 → ℕ → ENNReal → Prop

Given a function f : E → F, a formal multilinear series p and n : ℕ, we say that f has p as a finite power series on the ball of radius r > 0 around x if f (x + y) = ∑' pₘ yᵐ for all ‖y‖ < r and pₙ = 0 for n ≤ m.

Defined in

Mathlib.Analysis.Analytic.CPolynomialDef

Cited by

46 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace