`BookProof.ChapterLegendrePolynomial.legendre_deriv_coeff_parity` (l μ : ℕ) (h : μ ≤ l) (j : ℕ) (hpar : j % 2 ≠ (l - μ) % 2) : (derivative^[μ] (legendre l)).coeff j = 0

Proved

BookProof.ChapterLegendrePolynomial.legendre_deriv_coeff_parity

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLegendrePolynomial.

BookProof.ChapterLegendrePolynomial.legendre_deriv_coeff_parity (l μ : ℕ) (h : μ ≤ l) (j : ℕ) (hpar : j % 2 ≠ (l - μ) % 2) : (derivative^[μ] (legendre l)).coeff j = 0

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

Preamble

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



open Polynomial

Formal statement

theorem BookProof.ChapterLegendrePolynomial.legendre_deriv_coeff_parity (l μ : ℕ) (h : μ ≤ l) (j : ℕ)
    (hpar : j % 2 ≠ (l - μ) % 2) : (derivative^[μ] (legendre l)).coeff j = 0 := by sorry

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