Bennett positive weighted coeff mul

import Lean.Elab.Tactic.Omega
import Mathlib.Analysis.Analytic.Binomial
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Analysis.Normed.Ring.InfiniteSum
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring
import Mathlib.Topology.Algebra.InfiniteSum.Order

section
open Finset

namespace D1Bound5














theorem _root_.D1Bound5.bennett_positive_weighted_coeff_mul
    (P Q : PowerSeries ℝ) (r : ℝ) (n : ℕ) :
    (∑ ij ∈ Finset.antidiagonal n,
      (PowerSeries.coeff ij.1 P * r ^ ij.1) *
        (PowerSeries.coeff ij.2 Q * r ^ ij.2)) =
      PowerSeries.coeff n (P * Q) * r ^ n := by sorry







end D1Bound5
end