Function laguerre_function_series_slice 

pub fn laguerre_function_series_slice<P, E, V, const INT_ALPHA: bool>(
    x: V,
    alpha: V,
    alpha_int: i32,
    coeffs: &[E],
) -> V
where
    P: Policy,
    E: FloatElement,
    V: FloatVector<Element = E> + SpecializedSpecialMath<E>,

Runtime-length form of laguerre_function_series.

A genuine port of the recurrence rather than a fold over the const kernel: a series carries k-dependent state and does not partition the way the slice reductions in thermite do. Both forms must be edited together.

Same pre-scaling, same seed, same backward s_k order. Read laguerre_function_series for the reasoning. INT_ALPHA still selects the integer-weight path, but the weights are no longer folded literals at any alpha, since k is not a constant, so the per-step sqrt is paid in full here.

The empty series is 0, where the const form refuses to compile.