real_term

Function real_term 

Source
pub(super) fn real_term<const N: usize>(
    wave: Family,
    k: Jet<N>,
    r: [Jet<N>; 3],
    eta: Complex,
    mode: RealKambe<'_, N>,
) -> Jet<N>
Expand description

One real-space summand at the displacement r = -shift - R.

§Formula

Spherical: -i sqrt(2 / pi) k^l |r|^l Y_lm(r / |r|) I_(2l)(k |r|, eta), where |r|^l Y_lm is harmonic_normalization(l, m) times the solid harmonic. Cylindrical: -2 i / pi (-1)^m (k (x ± i y))^|m| I_(2|m| - 1)(k |r|, eta), with the sign (-1)^m and x - i y for negative m only.

RealKambe::SmallSplit stores first-order bounds on the absolute rounding errors that its Kambe integral leaves in its value and derivatives (see kambe_jet).