Theorems · Definition · complex analysis

FormalMultilinearSeries.sum

{𝕜 : Type u_1} →
  {E : Type u_3} →
    {F : Type u_4} →
      [inst : Semiring 𝕜] →
        [inst_1 : AddCommMonoid E] →
          [inst_2 : AddCommMonoid F] →
            [inst_3 : Module 𝕜 E] →
              [inst_4 : Module 𝕜 F] →
                [inst_5 : TopologicalSpace E] →
                  [inst_6 : TopologicalSpace F] →
                    [inst_7 : ContinuousAdd E] →
                      [inst_8 : ContinuousAdd F] →
                        [inst_9 : ContinuousConstSMul 𝕜 E] →
                          [inst_10 : ContinuousConstSMul 𝕜 F] → FormalMultilinearSeries 𝕜 E F → E → F

Given a formal multilinear series p and a vector x, then p.sum x is the sum Σ pₙ xⁿ. A priori, it only behaves well when ‖x‖ < p.radius.

Defined in

Mathlib.Analysis.Analytic.ConvergenceRadius

Cited by

34 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleTopologicalSpaceTopologicalSpaceContinuousAddContinuousAddContinuousConstSMulContinuousConstSMul