`BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel` (l : ℕ) {r : ℝ} (hr : r ≠ 0) : HasDerivAt (sbessel l) (r ^ l * ((l : ℝ) * gIter l r / r + deriv (gIter l) r)) r

Proved

BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalBesselODE.

BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel (l : ℕ) {r : ℝ} (hr : r ≠ 0) : HasDerivAt (sbessel l) (r ^ l * ((l : ℝ) * gIter l r / r + deriv (gIter l) r)) r

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

Preamble

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



open BookProof.ChapterSphericalBessel

Formal statement

theorem BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel (l : ℕ) {r : ℝ} (hr : r ≠ 0) :
    HasDerivAt (sbessel l) (r ^ l * ((l : ℝ) * gIter l r / r + deriv (gIter l) r)) r := by sorry

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