`BookProof.ChapterSolidHarmonic.radialFactor_euler` (e : E) (l μ : ℕ) (x : E) : fderiv ℝ (radialFactor e l μ) x x = ((l - μ : ℕ) : ℝ) * radialFactor e l μ x

Proved

BookProof.ChapterSolidHarmonic.radialFactor_euler

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSolidHarmonic.

BookProof.ChapterSolidHarmonic.radialFactor_euler (e : E) (l μ : ℕ) (x : E) : fderiv ℝ (radialFactor e l μ) x x = ((l - μ : ℕ) : ℝ) * radialFactor e l μ x

Formalization note: Lean 4 identifier BookProof.ChapterSolidHarmonic.radialFactor_euler.

Preamble

-- Generated from ChapterSolidHarmonic.lean — theorem BookProof.ChapterSolidHarmonic.radialFactor_euler
import Definitions.Def_ChapterLaplacianProduct
import Definitions.Def_ChapterSolidHarmonicTools
import Mathlib
import Definitions.Def_ChapterSolidHarmonic
import Definitions.Def_ChapterLegendrePolynomial
import Definitions.Def_ChapterRadialLaplacian
open BookProof.ChapterLegendrePolynomial
open BookProof.ChapterRadialLaplacian
open BookProof.ChapterSolidHarmonic



open Laplacian InnerProductSpace Polynomial
open BookProof.ChapterRadialLaplacian BookProof.ChapterLaplacianProduct
open BookProof.ChapterSolidHarmonicTools BookProof.ChapterLegendrePolynomial
open scoped RealInnerProductSpace

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]

Formal statement

theorem BookProof.ChapterSolidHarmonic.radialFactor_euler (e : E) (l μ : ℕ) (x : E) :
    fderiv ℝ (radialFactor e l μ) x x = ((l - μ : ℕ) : ℝ) * radialFactor e l μ x := by sorry

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