Theorems · Inductive type · several complex variables

HasFPowerSeriesOnBall

{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 → ENNReal → Prop

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

Defined in

Mathlib.Analysis.Analytic.Basic

Cited by

131 results in Mathlib

Foundations

Depth 163 from the axioms, rests on 3,363 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace