`BookProof.ChapterLegendrePolynomial.legendre_deriv_ode` (l μ : ℕ) : (X ^ 2 - 1) * derivative^[2] (derivative^[μ] (legendre l)) + C (2 * (μ : ℝ) + 2) * X * derivative (derivative^[

Proved

BookProof.ChapterLegendrePolynomial.legendre_deriv_ode

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLegendrePolynomial.

BookProof.ChapterLegendrePolynomial.legendre_deriv_ode (l μ : ℕ) : (X ^ 2 - 1) * derivative^[2] (derivative^[μ] (legendre l)) + C (2 * (μ : ℝ) + 2) * X * derivative (derivative^[μ] (legendre l)) + C ((μ : ℝ) * ((μ : ℝ) + 1) - (l : ℝ) * ((l : ℝ) + 1)) * derivative^[μ] (legendre l) = 0

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

Preamble

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



open Polynomial

Formal statement

theorem BookProof.ChapterLegendrePolynomial.legendre_deriv_ode (l μ : ℕ) :
    (X ^ 2 - 1) * derivative^[2] (derivative^[μ] (legendre l))
      + C (2 * (μ : ℝ) + 2) * X * derivative (derivative^[μ] (legendre l))
      + C ((μ : ℝ) * ((μ : ℝ) + 1) - (l : ℝ) * ((l : ℝ) + 1)) * derivative^[μ] (legendre l)
      = 0 := by sorry

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