Prove2Me

`BookProof.HermiteExpWall.gaussMoment_eq_integral` (k : ℕ) : gaussMoment k = ∫ x : ℝ, x ^ k * gaussW x

Proved
BookProof.HermiteExpWall.gaussMoment_eq_integral

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.gaussMoment_eq_integral (k : ℕ) : gaussMoment k = ∫ x : ℝ, x ^ k * gaussW x

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

Preamble
-- Generated from ChapterHermiteExpWall.lean — theorem BookProof.HermiteExpWall.gaussMoment_eq_integral
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterQgHermiteCore
import Mathlib
import Definitions.Def_ChapterHermiteExpWall
import Definitions.Def_ChapterHermiteFunctions
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteCore
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_eq_integral (k : ℕ) :
    gaussMoment k = ∫ x : ℝ, x ^ k * gaussW x := by sorry

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