`BookProof.HermiteExpWall.osc_psi` (m : ℕ) : (fun x => -deriv (deriv (psi (m + 2))) x + x ^ 2 / 4 * psi (m + 2) x) = gaussPoly (oscQ m (aCoef m) (bCoef m))

Proved

BookProof.HermiteExpWall.osc_psi

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.osc_psi (m : ℕ) : (fun x => -deriv (deriv (psi (m + 2))) x + x ^ 2 / 4 * psi (m + 2) x) = gaussPoly (oscQ m (aCoef m) (bCoef m))

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

Preamble

-- Generated from ChapterHermiteExpWall.lean — theorem BookProof.HermiteExpWall.osc_psi
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterHermiteProductCore
import Mathlib
import Definitions.Def_ChapterHermiteExpWall
import Definitions.Def_ChapterGhostField
import Definitions.Def_ChapterHermiteFunctions
import Definitions.Def_ChapterQgHermiteCore
open BookProof.GhostField
open BookProof.HermiteCore
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.osc_psi (m : ℕ) :
    (fun x => -deriv (deriv (psi (m + 2))) x + x ^ 2 / 4 * psi (m + 2) x)
      = gaussPoly (oscQ m (aCoef m) (bCoef m)) := by sorry

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