`BookProof.ChapterSolidHarmonic.contDiff_cylTerm` (e : E) (j m : ℕ) : ContDiff ℝ 2 fun y : E => (⟪e, y⟫_ℝ) ^ j * (‖y‖ ^ 2) ^ m

Proved

BookProof.ChapterSolidHarmonic.contDiff_cylTerm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSolidHarmonic.

BookProof.ChapterSolidHarmonic.contDiff_cylTerm (e : E) (j m : ℕ) : ContDiff ℝ 2 fun y : E => (⟪e, y⟫_ℝ) ^ j * (‖y‖ ^ 2) ^ m

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

Preamble

-- Generated from ChapterSolidHarmonic.lean — theorem BookProof.ChapterSolidHarmonic.contDiff_cylTerm
import Definitions.Def_ChapterLaplacianProduct
import Definitions.Def_ChapterSolidHarmonicTools
import Definitions.Def_ChapterLegendrePolynomial
import Mathlib
import Definitions.Def_ChapterSolidHarmonic
import Definitions.Def_ChapterRadialLaplacian
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.contDiff_cylTerm (e : E) (j m : ℕ) :
    ContDiff ℝ 2 fun y : E => (⟪e, y⟫_ℝ) ^ j * (‖y‖ ^ 2) ^ m := by sorry

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