  The gravitational deflection of test particles including light, due to a
radially moving Kerr-Newman black hole with an arbitrary constant velocity
being perpendicular to its angular momentum, is investigated. In harmonic
coordinates, we derive the second post-Minkowskian equations of motion for test
particles, and solve them by high-accuracy numerical calculations. We then
concentrate on discussing the kinematical corrections caused by the motion of
the gravitational source to the second-order deflection. The analytical formula
of light deflection angle up to second order by the moving lens is obtained.
For a massive particle moving with a relativistic velocity, there are two
different analytical results for Schwarzschild deflection angle up to second
order reported in the previous works, i.e.,
$\alpha(w)=2\left(1+\frac{1}{w^2}\right)\frac{M}{b}+3\pi\left(\frac{1}{4}+\frac{1}{w^2}\right)\frac{M^2}{b^2}$
and
$\alpha(w)=2\left(1+\frac{1}{w^2}\right)\frac{M}{b}+\left[3\pi\left(\frac{1}{4}+\frac{1}{w^2}\right)+2\left(1-\frac{1}{w^4}\right)\right]\frac{M^2}{b^2}$,
where $M,$ $b,$ and $w$ are the mass of the lens, impact parameter, and the
particle's initial velocity, respectively. Our numerical result is in perfect
agreement with the former. Furthermore, the analytical formula for massive
particle deflection up to second order in the Kerr geometry is achieved.
Finally, the possibilities of detecting the motion effects on the second-order
deflection are also analyzed.
