`BookProof.SqueezedGaussStates.tendsto_boundary` (ρ : ℝ) (h0 : 0 ≤ ρ) (h1 : ρ < 1) : Filter.Tendsto (fun M : ℕ => (2 * (M : ℝ) + 1) * ρ ^ M) Filter.atTop (nhds 0)

Proved

BookProof.SqueezedGaussStates.tendsto_boundary

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSqueezedGaussStates.

BookProof.SqueezedGaussStates.tendsto_boundary (ρ : ℝ) (h0 : 0 ≤ ρ) (h1 : ρ < 1) : Filter.Tendsto (fun M : ℕ => (2 * (M : ℝ) + 1) * ρ ^ M) Filter.atTop (nhds 0)

Formalization note: Lean 4 identifier BookProof.SqueezedGaussStates.tendsto_boundary.

Preamble

-- Generated from ChapterSqueezedGaussStates.lean — theorem BookProof.SqueezedGaussStates.tendsto_boundary
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterGaussCoordCombo
import Mathlib
import Definitions.Def_ChapterSqueezedGaussStates
open BookProof.SqueezedGaussStates



open MvPolynomial BookProof.HermiteProductCore BookProof.GaussCoordCombo

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.SqueezedGaussStates.tendsto_boundary (ρ : ℝ) (h0 : 0 ≤ ρ) (h1 : ρ < 1) :
    Filter.Tendsto (fun M : ℕ => (2 * (M : ℝ) + 1) * ρ ^ M) Filter.atTop (nhds 0) := by sorry

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