`BookProof.ChapterSolidHarmonic.fderiv_angularIm` (u v : E) (μ : ℕ) (x w : E) : fderiv ℝ (angularIm u v μ) x w = ((μ : ℂ) * (nullCLM u v x) ^ (μ - 1) * nullCLM u v w).im

Proved

BookProof.ChapterSolidHarmonic.fderiv_angularIm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSolidHarmonic.

BookProof.ChapterSolidHarmonic.fderiv_angularIm (u v : E) (μ : ℕ) (x w : E) : fderiv ℝ (angularIm u v μ) x w = ((μ : ℂ) * (nullCLM u v x) ^ (μ - 1) * nullCLM u v w).im

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

Preamble

-- Generated from ChapterSolidHarmonic.lean — theorem BookProof.ChapterSolidHarmonic.fderiv_angularIm
import Definitions.Def_ChapterRadialLaplacian
import Definitions.Def_ChapterLaplacianProduct
import Definitions.Def_ChapterSolidHarmonicTools
import Definitions.Def_ChapterLegendrePolynomial
import Mathlib
import Definitions.Def_ChapterSolidHarmonic
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.fderiv_angularIm (u v : E) (μ : ℕ) (x w : E) :
    fderiv ℝ (angularIm u v μ) x w = ((μ : ℂ) * (nullCLM u v x) ^ (μ - 1) * nullCLM u v w).im := by sorry

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