  Highly accurate closed-form expressions that describe the full trajectory of
photons propagating in the equatorial plane of a Kerr black hole are obtained
using asymptotic approximants. This work extends a prior study of the overall
bending angle for photons (Barlow, et al. 2017, Class. Quantum Grav., 34,
135017). The expressions obtained provide accurate trajectory predictions for
arbitrary spin and impact parameters, and provide significant time advantages
compared with numerical evaluation of the elliptic integrals that describe
photon trajectories. To construct approximants, asymptotic expansions for
photon deflection are required in various limits. To this end, complete
expansions are derived for the azimuthal angle as a function of radial distance
from the black hole in the far-distance and closest-approach (pericenter)
limits, and new coefficients are reported for the bending angle in the
weak-field limit (large impact parameter).
