`BookProof.HermiteExpWall.integrable_exp_mul_pow_gaussW` (c : ℝ) (k : ℕ) : Integrable (fun x : ℝ => Real.exp (c * x) * (x ^ k * gaussW x))

Proved

BookProof.HermiteExpWall.integrable_exp_mul_pow_gaussW

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.integrable_exp_mul_pow_gaussW (c : ℝ) (k : ℕ) : Integrable (fun x : ℝ => Real.exp (c * x) * (x ^ k * gaussW x))

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

Preamble

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



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

noncomputable section

Formal statement

theorem BookProof.HermiteExpWall.integrable_exp_mul_pow_gaussW (c : ℝ) (k : ℕ) :
    Integrable (fun x : ℝ => Real.exp (c * x) * (x ^ k * gaussW x)) := by sorry

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