Function legendre_series_slice 

pub fn legendre_series_slice<E, V>(x: V, coeffs: &[E]) -> V
where
    E: FloatElement,
    V: FloatVector<Element = E>,

Runtime-length form of legendre_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.

chebyshev_series no longer has a twin like this, its two bodies having been merged behind an N = 0 sentinel and an assert_unchecked. This one has not been merged, and the reason is a and b_next below. They are E::from_ratio calls, not const fns, so they become literals only when LLVM fully unrolls the loop. Chebyshev’s only per-step quantity is coeffs[k] and has nothing to lose, while merging here would put a division per step behind an assume that nothing would detect. Wants an asm or llvm-mca check before anyone tries it.

What the runtime length costs here is more than the lost unrolling: a_k and b_{k+1} are no longer compile-time constants, so each step pays a division to form them. If the degree is known, legendre_series is meaningfully cheaper, not just tidier.

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