`BookProof.ChapterLegendrePolynomial.legendre_deriv_coeff_eq_zero` (l μ k : ℕ) (h : l < k + μ) : (derivative^[μ] (legendre l)).coeff k = 0

Proved

BookProof.ChapterLegendrePolynomial.legendre_deriv_coeff_eq_zero

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_eq_zero (l μ k : ℕ) (h : l < k + μ) : (derivative^[μ] (legendre l)).coeff k = 0

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

Preamble

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



open Polynomial

Formal statement

theorem BookProof.ChapterLegendrePolynomial.legendre_deriv_coeff_eq_zero (l μ k : ℕ) (h : l < k + μ) :
    (derivative^[μ] (legendre l)).coeff k = 0 := by sorry

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