`BookProof.HermiteExpWall.gaussMoment_shift_eight` (N : ℕ) : gaussMoment (2 * N + 8) = ((2 * (N:ℝ)) + 7) * ((2 * (N:ℝ)) + 5) * ((2 * (N:ℝ)) + 3) * ((2 * (N:ℝ)) + 1) * gaussMoment (

Proved

BookProof.HermiteExpWall.gaussMoment_shift_eight

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.gaussMoment_shift_eight (N : ℕ) : gaussMoment (2 * N + 8) = ((2 * (N:ℝ)) + 7) * ((2 * (N:ℝ)) + 5) * ((2 * (N:ℝ)) + 3) * ((2 * (N:ℝ)) + 1) * gaussMoment (2 * N)

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

Preamble

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



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

noncomputable section

Formal statement

theorem BookProof.HermiteExpWall.gaussMoment_shift_eight (N : ℕ) : gaussMoment (2 * N + 8)
    = ((2 * (N:ℝ)) + 7) * ((2 * (N:ℝ)) + 5) * ((2 * (N:ℝ)) + 3) * ((2 * (N:ℝ)) + 1)
        * gaussMoment (2 * N) := by sorry

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