Unbound motion of massive particles in the Schwarzschild metric:
  Analytical description in case of strong deflection
  Deflection angles of massive test particles moving along an unbound
trajectory in the Schwarzschild metric are considered for the case of large
deflection. We analytically consider the strong deflection limit, which is
opposite to the commonly applied small deflection approximation and corresponds
to the situation when a massive particle moves from infinity, makes several
revolutions around a central object and goes to infinity. For this purpose we
rewrite an integral expression for the deflection angle as an explicit function
of the parameters determining the trajectory and expand it. Remarkably, in the
limiting case of strong deflection, we succeed in deriving for the first time
the analytical formulas for deflection angles as explicit functions of
parameters at infinity. In particular, we show that in this case the deflection
angle can be calculated as an explicit function of the impact parameter and
velocity at infinity beyond the usual assumption of small deflection.
