Function spherical_prefactor 

fn spherical_prefactor(z: Complex) -> Complex

sqrt(pi / 2z), which turns cylindrical functions of order l + 1/2 into spherical functions of order l.

On the negative real axis AMOS takes the limit from above for either sign of a zero imaginary part (it tests Im z < 0), where pi / 2z approaches the axis from below. Real-by-complex division gives pi / 2z a +0 imaginary part there, so the prefactor takes that side explicitly; the spherical functions are single-valued, and only the two factors’ agreement matters.