Function self_term 

pub(super) fn self_term<const N: usize>(
    wave: Family,
    k: Jet<N>,
    r: [Jet<N>; 3],
    eta: Complex,
) -> Jet<N>

The self term: the Cartesian Taylor term of real_Ewald(-r) - outgoing(-r) at the origin. Upstream zero2d (cylindrical) and zero3d (spherical) give its value at degree and order zero. Keeping its first-order polynomial gives the regular image-sum derivative at self.

Branch

Its incomplete gamma function of v = -1 / (2 eta^2) takes the sheet (self_sheet) of the principal ln((k eta)^2) of the real-space Kambe integrals less 2 ln k of the outgoing waves. For a sheet j turns off the principal one, DLMF 8.2.10 gives 2 Gamma(a) - Gamma(a, v) for half-integer a and odd j, and Gamma(-n, v) - 2 pi i j (-1)^n / n! for a = -n.