`BookProof.ChapterSphericalBesselODE.sbessel_recurrence` (l : ℕ) {r : ℝ} (hr : r ≠ 0) : sbessel l r + sbessel (l + 2) r = ((2 * (l + 1) + 1) / r) * sbessel (l + 1) r

Proved

BookProof.ChapterSphericalBesselODE.sbessel_recurrence

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalBesselODE.

BookProof.ChapterSphericalBesselODE.sbessel_recurrence (l : ℕ) {r : ℝ} (hr : r ≠ 0) : sbessel l r + sbessel (l + 2) r = ((2 * (l + 1) + 1) / r) * sbessel (l + 1) r

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

Preamble

-- Generated from ChapterSphericalBesselODE.lean — theorem BookProof.ChapterSphericalBesselODE.sbessel_recurrence
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_recurrence (l : ℕ) {r : ℝ} (hr : r ≠ 0) :
    sbessel l r + sbessel (l + 2) r = ((2 * (l + 1) + 1) / r) * sbessel (l + 1) r := by sorry

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