`BookProof.ChapterSphericalBesselODE.sbessel_radial_eigen` (l : ℕ) {p r : ℝ} (hp : p ≠ 0) (hr : r ≠ 0) : -(deriv (deriv (fun s => sbessel l (p * s))) r + (2 / r) * deriv (fun s =>

Proved

BookProof.ChapterSphericalBesselODE.sbessel_radial_eigen

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalBesselODE.

BookProof.ChapterSphericalBesselODE.sbessel_radial_eigen (l : ℕ) {p r : ℝ} (hp : p ≠ 0) (hr : r ≠ 0) : -(deriv (deriv (fun s => sbessel l (p * s))) r + (2 / r) * deriv (fun s => sbessel l (p * s)) r - ((l : ℝ) * (l + 1) / r ^ 2) * sbessel l (p * r)) = p ^ 2 * sbessel l (p * r)

Formalization note: Lean 4 identifier BookProof.ChapterSphericalBesselODE.sbessel_radial_eigen.

Preamble

-- Generated from ChapterSphericalBesselODE.lean — theorem BookProof.ChapterSphericalBesselODE.sbessel_radial_eigen
import Mathlib
import Definitions.Def_ChapterSphericalBesselODE
import Definitions.Def_ChapterSphericalBessel
open BookProof.ChapterSphericalBessel
open BookProof.ChapterSphericalBesselODE



open BookProof.ChapterSphericalBessel

Formal statement

theorem BookProof.ChapterSphericalBesselODE.sbessel_radial_eigen (l : ℕ) {p r : ℝ} (hp : p ≠ 0) (hr : r ≠ 0) :
    -(deriv (deriv (fun s => sbessel l (p * s))) r
        + (2 / r) * deriv (fun s => sbessel l (p * s)) r
        - ((l : ℝ) * (l + 1) / r ^ 2) * sbessel l (p * r))
      = p ^ 2 * sbessel l (p * r) := by sorry

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