`BookProof.GaussCoordCombo.pderiv_hermiteFactor_self` (i : Fin d) (n : ℕ) : pderiv i (hermiteFactor i (n + 1)) = ((n : ℂ) + 1) • hermiteFactor i n

Proved

BookProof.GaussCoordCombo.pderiv_hermiteFactor_self

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaussCoordCombo.

BookProof.GaussCoordCombo.pderiv_hermiteFactor_self (i : Fin d) (n : ℕ) : pderiv i (hermiteFactor i (n + 1)) = ((n : ℂ) + 1) • hermiteFactor i n

Formalization note: Lean 4 identifier BookProof.GaussCoordCombo.pderiv_hermiteFactor_self.

Preamble

-- Generated from ChapterGaussCoordCombo.lean — theorem BookProof.GaussCoordCombo.pderiv_hermiteFactor_self
import Mathlib
import Definitions.Def_ChapterGaussCoordCombo
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteProductCore
open BookProof.GaussCoordCombo



open MvPolynomial BookProof.HermiteProductCore

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.GaussCoordCombo.pderiv_hermiteFactor_self (i : Fin d) (n : ℕ) :
    pderiv i (hermiteFactor i (n + 1)) = ((n : ℂ) + 1) • hermiteFactor i n := by sorry

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