  Bending of light rays by gravitational sources is one of the first evidences
of the general relativity. When the gravitational souce is a stationary massive
object such as a black hole, the bending angle has an integral representation,
from which various series expansions in terms of the parameters of orbit and
the background spacetime has been derived. However, it is not clear that it has
any analytic expansion. In this paper, we show that such an analytic expansion
can be obtained for the case of a Schwarzschild black hole by solving an
inhomogeneous Picard-Fuchs equation, which has been applied to compute
effective superpotentials on D-branes in the Calabi-Yau manifolds. From the
analytic expression of the bending angle, both weak and strong deflection
expansions are explicitly obtained. We show that the result can be obtained by
the direct integration approach. We also discuss how the charge of the
gravitational source affects the bending angle and show that a similar analytic
expression can be obtained for the extremal Reissner-Nordstroem spacetime.
