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

Proved

BookProof.ChapterSphericalBesselODE.sbessel_rayleigh_raise

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalBesselODE.

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

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

Preamble

-- Generated from ChapterSphericalBesselODE.lean — theorem BookProof.ChapterSphericalBesselODE.sbessel_rayleigh_raise
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_rayleigh_raise (l : ℕ) {r : ℝ} (hr : r ≠ 0) :
    sbessel (l + 1) r = -(r ^ l) * deriv (fun s => sbessel l s / s ^ l) r := by sorry

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