`BookProof.ChapterLegendrePolynomial.rodrigues_step` (l : ℕ) : (X ^ 2 - 1) * derivative ((X ^ 2 - 1) ^ l) = C (2 * (l : ℝ)) * X * (X ^ 2 - 1) ^ l

Proved

BookProof.ChapterLegendrePolynomial.rodrigues_step

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLegendrePolynomial.

BookProof.ChapterLegendrePolynomial.rodrigues_step (l : ℕ) : (X ^ 2 - 1) * derivative ((X ^ 2 - 1) ^ l) = C (2 * (l : ℝ)) * X * (X ^ 2 - 1) ^ l

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

Preamble

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



open Polynomial

Formal statement

theorem BookProof.ChapterLegendrePolynomial.rodrigues_step (l : ℕ) :
    (X ^ 2 - 1) * derivative ((X ^ 2 - 1) ^ l) = C (2 * (l : ℝ)) * X * (X ^ 2 - 1) ^ l := by sorry

View graph