`BookProof.ChapterSphericalBesselODE.second_deriv_gIter` (l : ℕ) {r : ℝ} (hr : r ≠ 0) : deriv (deriv (gIter l)) r = -gIter (l + 1) r - r * deriv (gIter (l + 1)) r

Proved

BookProof.ChapterSphericalBesselODE.second_deriv_gIter

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalBesselODE.

BookProof.ChapterSphericalBesselODE.second_deriv_gIter (l : ℕ) {r : ℝ} (hr : r ≠ 0) : deriv (deriv (gIter l)) r = -gIter (l + 1) r - r * deriv (gIter (l + 1)) r

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

Preamble

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



open BookProof.ChapterSphericalBessel

Formal statement

theorem BookProof.ChapterSphericalBesselODE.second_deriv_gIter (l : ℕ) {r : ℝ} (hr : r ≠ 0) :
    deriv (deriv (gIter l)) r = -gIter (l + 1) r - r * deriv (gIter (l + 1)) r := by sorry

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