`BookProof.ChapterCoherentOccupation.hasSum_fallingTwo_expSeries` (lam : ℝ) : HasSum (fun n : ℕ => (n : ℝ) * ((n : ℝ) - 1) * (lam ^ n / (n ! : ℝ))) (lam ^ 2 * Real.exp lam)

Proved

BookProof.ChapterCoherentOccupation.hasSum_fallingTwo_expSeries

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOccupation.

BookProof.ChapterCoherentOccupation.hasSum_fallingTwo_expSeries (lam : ℝ) : HasSum (fun n : ℕ => (n : ℝ) * ((n : ℝ) - 1) * (lam ^ n / (n ! : ℝ))) (lam ^ 2 * Real.exp lam)

Formalization note: Lean 4 identifier BookProof.ChapterCoherentOccupation.hasSum_fallingTwo_expSeries.

Preamble

-- Generated from ChapterCoherentOccupation.lean — theorem BookProof.ChapterCoherentOccupation.hasSum_fallingTwo_expSeries
import Mathlib
import Definitions.Def_ChapterCoherentOccupation
open BookProof.ChapterCoherentOccupation


noncomputable section


open Real Nat ProbabilityTheory

Formal statement

theorem BookProof.ChapterCoherentOccupation.hasSum_fallingTwo_expSeries (lam : ℝ) :
    HasSum (fun n : ℕ => (n : ℝ) * ((n : ℝ) - 1) * (lam ^ n / (n ! : ℝ)))
      (lam ^ 2 * Real.exp lam) := by sorry

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