`BookProof.HarmonicOscillator.deriv_deriv_hermiteC` (n : ℕ) (x : ℝ) : deriv (deriv (hermiteC n)) x = ((hermiteNorm n : ℝ) : ℂ)⁻¹ * ((deriv (deriv (hermiteFun n)) x : ℝ) : ℂ)

Proved

BookProof.HarmonicOscillator.deriv_deriv_hermiteC

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHarmonicOscillatorEsa.

BookProof.HarmonicOscillator.deriv_deriv_hermiteC (n : ℕ) (x : ℝ) : deriv (deriv (hermiteC n)) x = ((hermiteNorm n : ℝ) : ℂ)⁻¹ * ((deriv (deriv (hermiteFun n)) x : ℝ) : ℂ)

Formalization note: Lean 4 identifier BookProof.HarmonicOscillator.deriv_deriv_hermiteC.

Preamble

-- Generated from ChapterHarmonicOscillatorEsa.lean — theorem BookProof.HarmonicOscillator.deriv_deriv_hermiteC
import Definitions.Def_ChapterStrichartzHermiteQG
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterHarmonicOscillatorEsa
import Definitions.Def_ChapterHermiteFunctions
open BookProof.HermiteCore
open BookProof.HarmonicOscillator



open MeasureTheory Polynomial BookProof.HermiteCore BookProof.HermiteStrichartzQG
open BookProof.FarisLavine

Formal statement

theorem BookProof.HarmonicOscillator.deriv_deriv_hermiteC (n : ℕ) (x : ℝ) :
    deriv (deriv (hermiteC n)) x
      = ((hermiteNorm n : ℝ) : ℂ)⁻¹ * ((deriv (deriv (hermiteFun n)) x : ℝ) : ℂ) := by sorry

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