Function half_integer_orders 

fn half_integer_orders<const N: usize>(
    reduced: &mut Reduced<N>,
    split: &Split,
    (factor, eta): (Complex, Complex),
    orders: i32,
    polynomial: impl Fn(i32) -> Jet<N>,
    plane_integrals: Option<&mut Vec<Option<Complex>>>,
) -> Jet<N>

sum_n factor (2 eta^2)^n F_(1/2 - n) P(n) over the half-integer orders n = 0..=orders of one reciprocal point with the degree polynomials P (zero ones skipped). Below every automatic split the orders weigh their terms, and are summed again from the single Kambe integrals where those bound the sum more tightly (Reduced::prefers_single).