Function laguerre_function_n 

pub fn laguerre_function_n<P, E, V, const N: usize, const INT_ALPHA: bool>(
    x: V,
    alpha: V,
    alpha_int: i32,
) -> V
where
    P: Policy,
    E: FloatElement,
    V: FloatVector<Element = E> + SpecializedSpecialMath<E>,

The orthonormal generalized Laguerre function $l_N^{(\alpha)}(x) = \sqrt{N!/\Gamma(N+\alpha+1)}\, x^{\alpha/2} e^{-x/2} L_N^{(\alpha)}(x)$.

Three-term recurrence on the functions themselves, with s_k = sqrt((k+1)(k+alpha+1)):

l_{k+1} = ((2k + alpha + 1 - x) l_k - s_{k-1} l_{k-1}) / s_k

which keeps every intermediate O(1). The s_k depend only on k and the weight, not on the running values, so they sit beside the recurrence rather than on its critical path. Under INT_ALPHA they are scalars and fold to literals at a compile-time weight; otherwise each step carries a vector sqrt and reciprocal. See [seed] for the range.