The lifetime Laplace exponent obtained from the driftless passage subordinator.

Reference: J. Bertoin, Lévy Processes, Cambridge University Press, 1996, Chapters IV and VIII.

theorem BGW.StableTrees.lintegral_one_sub_exp_lifetime {θ : ℝ} (hθ : 1 < θ ∧ θ ≤ 2) {q : ℝ} (hq : 0 ≤ q) : ∫⁻ (e : Excursion), ENNReal.ofReal (1 - Real.exp (-q * ↑e.lifetime)) ∂excursionMeasure θ = ENNReal.ofReal (q ^ (1 / θ))

Laplace exponent of the lifetime: ∫ (1 - e^{-q ζ}) dN = q^{1/θ} for q ≥ 0 (integrand in ℝ≥0∞; 1 - e^{-qζ} ∈ [0,1]).