`BookProof.HermiteExpWall.gaussPolyDeriv_two_monomial` (m : ℕ) : gaussPolyDeriv (gaussPolyDeriv ((Polynomial.X : Polynomial ℝ) ^ (m + 2))) = - kinQ m (aCoef m) (bCoef m)

Proved

BookProof.HermiteExpWall.gaussPolyDeriv_two_monomial

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.gaussPolyDeriv_two_monomial (m : ℕ) : gaussPolyDeriv (gaussPolyDeriv ((Polynomial.X : Polynomial ℝ) ^ (m + 2))) = - kinQ m (aCoef m) (bCoef m)

Formalization note: Lean 4 identifier BookProof.HermiteExpWall.gaussPolyDeriv_two_monomial.

Preamble

-- Generated from ChapterHermiteExpWall.lean — theorem BookProof.HermiteExpWall.gaussPolyDeriv_two_monomial
import Definitions.Def_ChapterHermiteFunctions
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterHermiteProductCore
import Mathlib
import Definitions.Def_ChapterHermiteExpWall
import Definitions.Def_ChapterQgHermiteCore
open BookProof.QgHermiteCore
open BookProof.HermiteExpWall



open MeasureTheory Polynomial
open BookProof.HermiteCore BookProof.Starobinsky BookProof.QgHermiteCore
open BookProof.HermiteProductCore

noncomputable section

Formal statement

theorem BookProof.HermiteExpWall.gaussPolyDeriv_two_monomial (m : ℕ) :
    gaussPolyDeriv (gaussPolyDeriv ((Polynomial.X : Polynomial ℝ) ^ (m + 2)))
      = - kinQ m (aCoef m) (bCoef m) := by sorry

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