Function gauss_laguerre_impl 

pub fn gauss_laguerre_impl<P, E, V>(k: V, alpha: V, n: u32) -> (V, V)
where
    P: Policy,
    E: FloatElement,
    V: FloatVector<Element = E> + SpecializedSpecialMath<E>,

The k-th node and weight of the n-point Gauss-Laguerre rule (weight x^alpha e^{-x} on [0, inf)), k per lane, k = 0 the largest root, alpha > -1 per lane.

Seed: the WKB phase of the Laguerre equation with x = nu cos^2(psi/2), nu = 4n + 2 alpha + 2, psi - sin psi = 4 pi (k + 3/4)/nu, five Newton steps from psi = (6c)^{1/3}. The count of phase between the two turning points is n + alpha/2 + 1/2, which is the Bessel-zero offset alpha/2 - 1/4 on the left and the Airy 3/4 on the right, so the seed is uniformly within a fraction of a root spacing. Newton on the raw L_m^alpha, (m+1) L_{m+1} = (2m + alpha + 1 - x) L_m - (m + alpha) L_{m-1}, scalar divisor, with x L_n' = n L_n - (n + alpha) L_{n-1}. Weight from Hildebrand’s w = Gamma(n + alpha + 1) / (n! x L_n'(x_k)^2), the Gamma ratio as the running product Gamma(alpha + 1) prod (m + alpha)/m. L_{n-1} at the largest root grows like e^{x/2}, which bounds the rule near n = 170 in f64 and n = 20 in f32.