`BookProof.ChapterLegendrePolynomial.coeff_iterD_two` (Y : ℝ[X]) (j : ℕ) : (derivative^[2] Y).coeff j = (((j : ℝ) + 2) * ((j : ℝ) + 1)) * Y.coeff (j + 2)

Proved

BookProof.ChapterLegendrePolynomial.coeff_iterD_two

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLegendrePolynomial.

BookProof.ChapterLegendrePolynomial.coeff_iterD_two (Y : ℝ[X]) (j : ℕ) : (derivative^[2] Y).coeff j = (((j : ℝ) + 2) * ((j : ℝ) + 1)) * Y.coeff (j + 2)

Formalization note: Lean 4 identifier BookProof.ChapterLegendrePolynomial.coeff_iterD_two.

Preamble

-- Generated from ChapterLegendrePolynomial.lean — theorem BookProof.ChapterLegendrePolynomial.coeff_iterD_two
import Mathlib
import Definitions.Def_ChapterLegendrePolynomial
open BookProof.ChapterLegendrePolynomial



open Polynomial

Formal statement

theorem BookProof.ChapterLegendrePolynomial.coeff_iterD_two (Y : ℝ[X]) (j : ℕ) :
    (derivative^[2] Y).coeff j = (((j : ℝ) + 2) * ((j : ℝ) + 1)) * Y.coeff (j + 2) := by sorry

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